Showing 1–50 of 448 results

Is Winter Coming?

Authors: A. Winter, A. Winter, A. Winter, A. Winter

Abstract: We critically examine the often-made observation that "quantum winter [or some other winter] is coming", and the related admonition to prepare for this or that winter, inevitably bound to arrive. What we find based on even the most superficial look at the available evidence is that such statements not only are overblown hype, but are also factually wrong: Winter is here, and the real question is r… ▽ More We critically examine the often-made observation that "quantum winter [or some other winter] is coming", and the related admonition to prepare for this or that winter, inevitably bound to arrive. What we find based on even the most superficial look at the available evidence is that such statements not only are overblown hype, but are also factually wrong: Winter is here, and the real question is rather for how long it/they will stay. △ Less

Submitted 29 March, 2024; originally announced March 2024.

Comments: 2 pages

Comparative Microscopic Study of Entropies and their Production

Authors: Philipp Strasberg, Joseph Schindler

Abstract: We study the time evolution of eleven microscopic entropy definitions (of Boltzmann-surface, Gibbs-volume, canonical, coarse-grained-observational, entanglement and diagonal type) and three microscopic temperature definitions (based on Boltzmann, Gibbs or canonical entropy). This is done for the archetypal nonequilibrium setup of two systems exchanging energy, modeled here with random matrix theor… ▽ More We study the time evolution of eleven microscopic entropy definitions (of Boltzmann-surface, Gibbs-volume, canonical, coarse-grained-observational, entanglement and diagonal type) and three microscopic temperature definitions (based on Boltzmann, Gibbs or canonical entropy). This is done for the archetypal nonequilibrium setup of two systems exchanging energy, modeled here with random matrix theory, based on numerical integration of the Schroedinger equation. We consider three types of pure initial states (local energy eigenstates, decorrelated and entangled microcanonical states) and three classes of systems: (A) two normal systems, (B) a normal and a negative temperature system and (C) a normal and a negative heat capacity system. We find: (1) All types of initial states give rise to the same macroscopic dynamics. (2) Entanglement and diagonal entropy sensitively depend on the microstate, in contrast to all other entropies. (3) For class B and C, Gibbs-volume entropies can violate the second law and the associated temperature becomes meaningless. (4) For class C, Boltzmann-surface entropies can violate the second law and the associated temperature becomes meaningless. (5) Canonical entropy has a tendency to remain almost constant. (6) For a Haar random initial state, entanglement or diagonal entropy behave similar or identical to coarse-grained-observational entropy. △ Less

Submitted 14 March, 2024; originally announced March 2024.

Comments: 14.5 pages with big figures plus references. Comments and discussion very welcome!

Multipartite entanglement in the diagonal symmetric subspace

Authors: Jordi Romero-Pallejà, Jennifer Ahiable, Alessandro Romancino, Carlo Marconi, Anna Sanpera

Abstract: We investigate the entanglement properties in the symmetric subspace of $N$-partite $d$-dimensional systems (qudits). For diagonal symmetric states, we show that there is no bound entanglement for $d = 3,4 $ and $N = 3$. Further, we present a constructive algorithm to map multipartite diagonal symmetric states of qudits onto bipartite symmetric states of larger local dimension. This technique grea… ▽ More We investigate the entanglement properties in the symmetric subspace of $N$-partite $d$-dimensional systems (qudits). For diagonal symmetric states, we show that there is no bound entanglement for $d = 3,4 $ and $N = 3$. Further, we present a constructive algorithm to map multipartite diagonal symmetric states of qudits onto bipartite symmetric states of larger local dimension. This technique greatly simplifies the analysis of multipartite states and allows to infer entanglement properties for any even $N \geq 4 $ due to the fact that the PPT conditions that arise from the bipartite symmetric state correspond to the same PPT conditions that appear in the multipartite diagonal symmetric state. △ Less

Submitted 8 March, 2024; originally announced March 2024.

Comments: 7 pages, 2 figures, to be submitted

Quantum Wiretap Channel Coding Assisted by Noisy Correlation

Authors: Minglai Cai, Andreas Winter

Abstract: We consider the private classical capacity of a quantum wiretap channel, where the users (sender Alice, receiver Bob, and eavesdropper Eve) have access to the resource of a shared quantum state, additionally to their channel inputs and outputs. An extreme case is maximal entanglement or a secret key between Alice and Bob, both of which would allow for onetime padding the message. But here both the… ▽ More We consider the private classical capacity of a quantum wiretap channel, where the users (sender Alice, receiver Bob, and eavesdropper Eve) have access to the resource of a shared quantum state, additionally to their channel inputs and outputs. An extreme case is maximal entanglement or a secret key between Alice and Bob, both of which would allow for onetime padding the message. But here both the wiretap channel and the shared state are general. In the other extreme case that the state is trivial, we recover the wiretap channel and its private capacity [N. Cai, A. Winter and R. W. Yeung, Probl. Inform. Transm. 40(4):318-336, 2004]. We show how to use the given resource state to build a code for secret classical communication. Our main result is a lower bound on the assisted private capacity, which asymptotically meets the multi-letter converse and which encompasses all sorts of previous results as special cases. △ Less

Submitted 20 February, 2024; originally announced February 2024.

Deterministic identification over channels with finite output: a dimensional perspective on superlinear rates

Authors: Pau Colomer, Christian Deppe, Holger Boche, Andreas Winter

Abstract: Following initial work by JaJa and Ahlswede/Cai, and inspired by a recent renewed surge in interest in deterministic identification via noisy channels, we consider the problem in its generality for memoryless channels with finite output, but arbitrary input alphabets. Such a channel is essentially given by (the closure of) the subset of its output distributions in the probability simplex. Our ma… ▽ More Following initial work by JaJa and Ahlswede/Cai, and inspired by a recent renewed surge in interest in deterministic identification via noisy channels, we consider the problem in its generality for memoryless channels with finite output, but arbitrary input alphabets. Such a channel is essentially given by (the closure of) the subset of its output distributions in the probability simplex. Our main findings are that the maximum number of messages thus identifiable scales super-exponentially as $2^{R\,n\log n}$ with the block length $n$, and that the optimal rate $R$ is upper and lower bounded in terms of the covering (aka Minkowski, or Kolmogorov, or entropy) dimension $d$ of the output set: $\frac14 d \leq R \leq d$. Leading up to the general case, we treat the important special case of the so-called Bernoulli channel with input alphabet $[0;1]$ and binary output, which has $d=1$, to gain intuition. Along the way, we show a certain Hypothesis Testing Lemma (generalising an earlier insight of Ahlswede regarding the intersection of typical sets) that implies that for the construction of a deterministic identification code, it is sufficient to ensure pairwise reliable distinguishability of the output distributions. These results are then shown to generalise directly to classical-quantum channels with finite-dimensional output quantum system (but arbitrary input alphabet), and in particular to quantum channels on finite-dimensional quantum systems under the constraint that the identification code can only use tensor product inputs. △ Less

Submitted 14 February, 2024; originally announced February 2024.

Comments: 24 pages, 3 figures

Zero-entropy encoders and simultaneous decoders in identification via quantum channels

Authors: Pau Colomer, Christian Deppe, Holger Boche, Andreas Winter

Abstract: Motivated by deterministic identification via (classical) channels, where the encoder is not allowed to use randomization, we revisit the problem of identification via quantum channels but now with the additional restriction that the message encoding must use pure quantum states, rather than general mixed states. Together with the previously considered distinction between simultaneous and general… ▽ More Motivated by deterministic identification via (classical) channels, where the encoder is not allowed to use randomization, we revisit the problem of identification via quantum channels but now with the additional restriction that the message encoding must use pure quantum states, rather than general mixed states. Together with the previously considered distinction between simultaneous and general decoders, this suggests a two-dimensional spectrum of different identification capacities, whose behaviour could a priori be very different. We demonstrate two new results as our main findings: first, we show that all four combinations (pure/mixed encoder, simultaneous/general decoder) have a double-exponentially growing code size, and that indeed the corresponding identification capacities are lower bounded by the classical transmission capacity for a general quantum channel, which is given by the Holevo-Schumacher-Westmoreland Theorem. Secondly, we show that the simultaneous identification capacity of a quantum channel equals the simultaneous identification capacity with pure state encodings, thus leaving three linearly ordered identification capacities. By considering some simple examples, we finally show that these three are all different: general identification capacity can be larger than pure-state-encoded identification capacity, which in turn can be larger than pure-state-encoded simultaneous identification capacity. △ Less

Submitted 14 February, 2024; originally announced February 2024.

Comments: 20 pages, 1 figure

Fundamental limits of metrology at thermal equilibrium

Authors: Paolo Abiuso, Pavel Sekatski, John Calsamiglia, Martí Perarnau-Llobet

Abstract: We consider the estimation of an unknown parameter $θ$ through a quantum probe at thermal equilibrium. The probe is assumed to be in a Gibbs state according to its Hamiltonian $H_θ$, which is divided in a parameter-encoding term $H^P_θ$ and an additional, parameter-independent, control $H^C$. Given a fixed encoding, we find the maximal Quantum Fisher Information attainable via arbitrary $H^C$, whi… ▽ More We consider the estimation of an unknown parameter $θ$ through a quantum probe at thermal equilibrium. The probe is assumed to be in a Gibbs state according to its Hamiltonian $H_θ$, which is divided in a parameter-encoding term $H^P_θ$ and an additional, parameter-independent, control $H^C$. Given a fixed encoding, we find the maximal Quantum Fisher Information attainable via arbitrary $H^C$, which provides a fundamental bound on the measurement precision. Our bounds show that: (i) assuming full control of $H^C$, quantum non-commutativity does not offer any fundamental advantage in the estimation of $θ$; (ii) an exponential quantum advantage arises at low temperatures if $H^C$ is constrained to have a spectral gap; (iii) in the case of locally-encoded parameters, the optimal sensitivity presents a Heisenberg-like $N^2$-scaling in terms of the number of particles of the probe, which can be reached with local measurements. We apply our results to paradigmatic spin chain models, showing that these fundamental limits can be approached using local two-body interactions. Our results set the fundamental limits and optimal control for metrology with thermal and ground state probes, including probes at the verge of criticality. △ Less

Submitted 9 February, 2024; originally announced February 2024.

Comments: Comments welcome!

Robust generation of $N$-partite $N$-level singlet states by identical particle interferometry

Authors: Matteo Piccolini, Marcin Karczewski, Andreas Winter, Rosario Lo Franco

Abstract: We propose an interferometric scheme for generating the totally antisymmetric state of $N$ identical bosons with $N$ internal levels (generalized singlet). This state is a resource for various problems with dramatic quantum advantage. The procedure uses a sequence of Fourier multi-ports, combined with coincidence measurements filtering the results. Successful preparation of the generalized singlet… ▽ More We propose an interferometric scheme for generating the totally antisymmetric state of $N$ identical bosons with $N$ internal levels (generalized singlet). This state is a resource for various problems with dramatic quantum advantage. The procedure uses a sequence of Fourier multi-ports, combined with coincidence measurements filtering the results. Successful preparation of the generalized singlet is confirmed when the $N$ particles of the input state stay separate (anti-bunch) on each multiport. The scheme is robust to local lossless noise and works even with a totally mixed input state. △ Less

Submitted 8 January, 2024; v1 submitted 28 December, 2023; originally announced December 2023.

Comments: 5+2 pages, 1 figure

Quantum multi-anomaly detection

Authors: Santiago Llorens, Gael Sentís, Ramon Muñoz-Tapia

Abstract: A source assumed to prepare a specified reference state sometimes prepares an anomalous one. We address the task of identifying these anomalous states in a series of $n$ preparations with $k$ anomalies. We analyse the minimum-error protocol and the zero-error (unambiguous) protocol and obtain closed expressions for the success probability when both reference and anomalous states are known to the o… ▽ More A source assumed to prepare a specified reference state sometimes prepares an anomalous one. We address the task of identifying these anomalous states in a series of $n$ preparations with $k$ anomalies. We analyse the minimum-error protocol and the zero-error (unambiguous) protocol and obtain closed expressions for the success probability when both reference and anomalous states are known to the observer and anomalies can appear equally likely in any position of the preparation series. We find the solution using results from association schemes theory. In particular we use the Johnson association scheme which arises naturally from the Gram matrix of this problem. We also study the regime of large $n$ and obtain the expression of the success probability that is non-vanishing. Finally, we address the case in which the observer is blind to the reference and the anomalous states. This scenario requires an universal protocol for which we prove that in the asymptotic limit the success probability correspond to average of the known state scenario. △ Less

Submitted 20 December, 2023; originally announced December 2023.

Comments: 9 pages, 4 figures, comments are welcome

Learning finitely correlated states: stability of the spectral reconstruction

Authors: Marco Fanizza, Niklas Galke, Josep Lumbreras, Cambyse Rouzé, Andreas Winter

Abstract: We show that marginals of subchains of length $t$ of any finitely correlated translation invariant state on a chain can be learned, in trace distance, with $O(t^2)$ copies -- with an explicit dependence on local dimension, memory dimension and spectral properties of a certain map constructed from the state -- and computational complexity polynomial in $t$. The algorithm requires only the estimatio… ▽ More We show that marginals of subchains of length $t$ of any finitely correlated translation invariant state on a chain can be learned, in trace distance, with $O(t^2)$ copies -- with an explicit dependence on local dimension, memory dimension and spectral properties of a certain map constructed from the state -- and computational complexity polynomial in $t$. The algorithm requires only the estimation of a marginal of a controlled size, in the worst case bounded by a multiple of the minimum bond dimension, from which it reconstructs a translation invariant matrix product operator. In the analysis, a central role is played by the theory of operator systems. A refined error bound can be proven for $C^*$-finitely correlated states, which have an operational interpretation in terms of sequential quantum channels applied to the memory system. We can also obtain an analogous error bound for a class of matrix product density operators reconstructible by local marginals. In this case, a linear number of marginals must be estimated, obtaining a sample complexity of $\tilde{O}(t^3)$. The learning algorithm also works for states that are only close to a finitely correlated state, with the potential of providing competitive algorithms for other interesting families of states. △ Less

Submitted 12 December, 2023; originally announced December 2023.

Comments: 27+7 pages, 6 figures

Simplifying the simulation of local Hamiltonian dynamics

Authors: Ayaka Usui, Anna Sanpera, María García Díaz

Abstract: Local Hamiltonians, $H_k$, describe non-trivial $k$-body interactions in quantum many-body systems. Here, we address the dynamical simulatability of a $k$-local Hamiltonian by a simpler one, $H_{k'}$, with $k'<k$, under the realistic constraint that both Hamiltonians act on the same Hilbert space. When it comes to exact simulation, we build upon known methods to derive examples of $H_k$ and… ▽ More Local Hamiltonians, $H_k$, describe non-trivial $k$-body interactions in quantum many-body systems. Here, we address the dynamical simulatability of a $k$-local Hamiltonian by a simpler one, $H_{k'}$, with $k'<k$, under the realistic constraint that both Hamiltonians act on the same Hilbert space. When it comes to exact simulation, we build upon known methods to derive examples of $H_k$ and $H_{k'}$ that simulate the same physics. We also address the most realistic case of approximate simulation. There, we upper-bound the error up to which a Hamiltonian can simulate another one, regardless of their internal structure, and prove, by means of an example, that the accuracy of a $(k'=2)$-local Hamiltonian to simulate $H_{k}$ with $k>2$ increases with $k$. Finally, we propose a method to search for the $k'$-local Hamiltonian that simulates, with the highest possible precision, the short time dynamics of a given $H_k$ Hamiltonian. △ Less

Submitted 10 October, 2023; originally announced October 2023.

Comments: 7 pages, 4 figures

Shearing Off the Tree: Emerging Branch Structure and Born's Rule in an Equilibrated Multiverse

Authors: Philipp Strasberg, Joseph Schindler

Abstract: Within the many worlds interpretation (MWI) it is believed that, as time passes on, the linearity of the Schrödinger equation together with decoherence generate an exponentially growing tree of branches where "everything happens", provided the branches are defined for a decohering basis. By studying an example, using exact numerical diagonalization of the Schrödinger equation to compute the decohe… ▽ More Within the many worlds interpretation (MWI) it is believed that, as time passes on, the linearity of the Schrödinger equation together with decoherence generate an exponentially growing tree of branches where "everything happens", provided the branches are defined for a decohering basis. By studying an example, using exact numerical diagonalization of the Schrödinger equation to compute the decoherent histories functional, we find that this picture needs revision. Our example shows decoherence for histories defined at a few times, but a significant fraction (often the vast majority) of branches shows strong interference effects for histories of many times. In a sense made precise below, the histories independently sample an equilibrated quantum process, and, remarkably, we find that only histories that sample frequencies in accordance with Born's rule remain decoherent. Our results suggest that there is more structure in the many worlds tree than previously anticipated, influencing arguments of both proponents and opponents of the MWI. △ Less

Submitted 21 November, 2023; v1 submitted 10 October, 2023; originally announced October 2023.

Comments: Various slight changes in the presentation to improve clarity. Still 4.5 pages with 4 figures and a mini appendix. Constructive criticism and comments welcome!

Optical fibres with memory effects and their quantum communication capacities

Authors: Francesco Anna Mele, Giacomo De Palma, Marco Fanizza, Vittorio Giovannetti, Ludovico Lami

Abstract: The development of quantum repeaters poses significant challenges in terms of cost and maintenance, prompting the exploration of alternative approaches for achieving long-distance quantum communication. In the absence of quantum repeaters and under the memoryless (iid) approximation, it has been established that some fundamental quantum communication tasks are impossible if the transmissivity of a… ▽ More The development of quantum repeaters poses significant challenges in terms of cost and maintenance, prompting the exploration of alternative approaches for achieving long-distance quantum communication. In the absence of quantum repeaters and under the memoryless (iid) approximation, it has been established that some fundamental quantum communication tasks are impossible if the transmissivity of an optical fibre falls below a known critical value, resulting in a severe constraint on the achievable distance for quantum communication. However, if the memoryless assumption does not hold -- e.g. when input signals are separated by a sufficiently short time interval -- the validity of this limitation is put into question. In this paper we introduce a model of optical fibre that can describe memory effects for long transmission lines. We then solve its quantum capacity, two-way quantum capacity, and secret-key capacity exactly. By doing so, we show that -- due to the memory cross-talk between the transmitted signals -- reliable quantum communication is attainable even for highly noisy regimes where it was previously considered impossible. As part of our solution, we find the critical time interval between subsequent signals below which quantum communication, two-way entanglement distribution, and quantum key distribution become achievable. △ Less

Submitted 29 September, 2023; originally announced September 2023.

Comments: 36 pages, 7 figures

Microscopic contributions to the entropy production at all times: From nonequilibrium steady states to global thermalization

Authors: Ayaka Usui, Krzysztof Ptaszyński, Massimiliano Esposito, Philipp Strasberg

Abstract: Based on exact integration of the Schrödinger equation, we numerically study microscopic contributions to the entropy production for the single electron transistor, a paradigmatic model describing a single Fermi level tunnel coupled to two baths of free fermions. To this end, we decompose the entropy production into a sum of information theoretic terms and study them across all relevant time scale… ▽ More Based on exact integration of the Schrödinger equation, we numerically study microscopic contributions to the entropy production for the single electron transistor, a paradigmatic model describing a single Fermi level tunnel coupled to two baths of free fermions. To this end, we decompose the entropy production into a sum of information theoretic terms and study them across all relevant time scales, including the nonequilibrium steady state regime and the final stage of global thermalization. We find that the entropy production is dominated for most times by microscopic deviations from thermality in the baths and the correlation between (but not inside) the baths. Despite these microscopic deviations from thermality, the temperatures and chemical potentials of the baths thermalize as expected, even though our model is integrable. Importantly, this observation is confirmed for both initially mixed and pure states. We further observe that the bath-bath correlations are quite insensitive to the system-bath coupling strength contrary to intuition. Finally, the system-bath correlation, small in an absolute sense, dominates in a relative sense and displays pure quantum correlations for all studied parameter regimes. △ Less

Submitted 23 February, 2024; v1 submitted 21 September, 2023; originally announced September 2023.

Comments: 12 pages, 9 figures

Journal ref: New J. Phys. 26 023049 (2024)

Geometry of entanglement and separability in Hilbert subspaces of dimension up to three

Authors: Rotem Liss, Tal Mor, Andreas Winter

Abstract: We present a complete classification of the geometry of entangled and separable states in three-dimensional Hilbert subspaces of bipartite and multipartite quantum systems. Our analysis begins by finding the geometric structure of the pure product states in a given three-dimensional Hilbert subspace, which determines all the possible separable and entangled mixed states over the same subspace. In… ▽ More We present a complete classification of the geometry of entangled and separable states in three-dimensional Hilbert subspaces of bipartite and multipartite quantum systems. Our analysis begins by finding the geometric structure of the pure product states in a given three-dimensional Hilbert subspace, which determines all the possible separable and entangled mixed states over the same subspace. In bipartite systems, we characterise the 14 possible qualitatively different geometric shapes for the set of separable states in any three-dimensional Hilbert subspace (5 classes which also appear in two-dimensional subspaces and were found and analysed by Boyer, Liss and Mor [Phys. Rev. A 95:032308, 2017], and 9 novel classes which appear only in three-dimensional subspaces), describe their geometries, and provide figures illustrating them. We also generalise these results to characterise the sets of fully separable and entangled states in three-dimensional subspaces of multipartite systems. Our results show which geometrical forms quantum entanglement can and cannot take in low-dimensional subspaces. △ Less

Submitted 10 September, 2023; originally announced September 2023.

Comments: 24 pages; 5 figures

Comment on "Extending the Laws of Thermodynamics for Arbitrary Autonomous Quantum Systems"

Authors: Philipp Strasberg

Abstract: Recently, Elouard and Lombard Latune [PRX Quantum 4, 020309 (2023)] claimed to extend the laws of thermodynamics to "arbitrary quantum systems" valid "at any scale" using "consistent" definitions allowing them to "recover known results" from the literature. I show that their definitions are in conflict with textbook thermodynamics and over- or underestimate the real entropy production by orders of… ▽ More Recently, Elouard and Lombard Latune [PRX Quantum 4, 020309 (2023)] claimed to extend the laws of thermodynamics to "arbitrary quantum systems" valid "at any scale" using "consistent" definitions allowing them to "recover known results" from the literature. I show that their definitions are in conflict with textbook thermodynamics and over- or underestimate the real entropy production by orders of magnitude. The cause of this problem is traced back to problematic definitions of entropy and temperature, the latter, for instance, violates the zeroth law. It is pointed out that another framework presented in PRX Quantum 2, 030202 (2021) does not suffer from these problems, while Elouard and Lombard Latune falsely claim that it only provides a positive entropy production for a smaller class of initial states. A simple way to unify both approaches is also presented. △ Less

Submitted 8 September, 2023; originally announced September 2023.

Comments: 2 pages

New Protocols for Conference Key and Multipartite Entanglement Distillation

Authors: Farzin Salek, Andreas Winter

Abstract: We approach two interconnected problems of quantum information processing in networks: Conference key agreement and entanglement distillation, both in the so-called source model where the given resource is a multipartite quantum state and the players interact over public classical channels to generate the desired correlation. The first problem is the distillation of a conference key when the sourc… ▽ More We approach two interconnected problems of quantum information processing in networks: Conference key agreement and entanglement distillation, both in the so-called source model where the given resource is a multipartite quantum state and the players interact over public classical channels to generate the desired correlation. The first problem is the distillation of a conference key when the source state is shared between a number of legal players and an eavesdropper; the eavesdropper, apart from starting off with this quantum side information, also observes the public communication between the players. The second is the distillation of Greenberger-Horne-Zeilinger (GHZ) states by means of local operations and classical communication (LOCC) from the given mixed state. These problem settings extend our previous paper [IEEE Trans. Inf. Theory 68(2):976-988, 2022], and we generalise its results: using a quantum version of the task of communication for omniscience, we derive novel lower bounds on the distillable conference key from any multipartite quantum state by means of non-interacting communication protocols. Secondly, we establish novel lower bounds on the yield of GHZ states from multipartite mixed states. Namely, we present two methods to produce bipartite entanglement between sufficiently many nodes so as to produce GHZ states. Next, we show that the conference key agreement protocol can be made coherent under certain conditions, enabling the direct generation of multipartite GHZ states. △ Less

Submitted 2 August, 2023; originally announced August 2023.

Bounding the joint numerical range of Pauli strings by graph parameters

Authors: Zhen-Peng Xu, René Schwonnek, Andreas Winter

Abstract: The interplay between the quantum state space and a specific set of measurements can be effectively captured by examining the set of jointly attainable expectation values. This set is commonly referred to as the (convex) joint numerical range. In this work, we explore geometric properties of this construct for measurements represented by tensor products of Pauli observables, also known as Pauli st… ▽ More The interplay between the quantum state space and a specific set of measurements can be effectively captured by examining the set of jointly attainable expectation values. This set is commonly referred to as the (convex) joint numerical range. In this work, we explore geometric properties of this construct for measurements represented by tensor products of Pauli observables, also known as Pauli strings. The structure of pairwise commutation and anticommutation relations among a set of Pauli strings determines a graph $G$, sometimes also called the frustration graph. We investigate the connection between the parameters of this graph and the structure of minimal ellipsoids encompassing the joint numerical range. Such an outer approximation can be very practical since ellipsoids can be handled analytically even in high dimensions. We find counterexamples to a conjecture from [C. de Gois, K. Hansenne and O. Gühne, arXiv:2207.02197], and answer an open question in [M. B. Hastings and R. O'Donnell, Proc. STOC 2022, pp. 776-789], which implies a new graph parameter that we call $β(G)$. Besides, we develop this approach in different directions, such as comparison with graph-theoretic approaches in other fields, applications in quantum information theory, numerical methods, properties of the new graph parameter, etc. Our approach suggests many open questions that we discuss briefly at the end. △ Less

Submitted 1 August, 2023; originally announced August 2023.

Comments: 14+3 pages, 5 figures

Report number: 1337

Sequential hypothesis testing for continuously-monitored quantum systems

Authors: Giulio Gasbarri, Matias Bilkis, Elisabet Roda-Salichs, John Calsamiglia

Abstract: We consider a quantum system that is being continuously monitored, giving rise to a measurement signal. From such a stream of data, information needs to be inferred about the underlying system's dynamics. Here we focus on hypothesis testing problems and put forward the usage of sequential strategies where the signal is analyzed in real time, allowing the experiment to be concluded as soon as the u… ▽ More We consider a quantum system that is being continuously monitored, giving rise to a measurement signal. From such a stream of data, information needs to be inferred about the underlying system's dynamics. Here we focus on hypothesis testing problems and put forward the usage of sequential strategies where the signal is analyzed in real time, allowing the experiment to be concluded as soon as the underlying hypothesis can be identified with a certified prescribed success probability. We analyze the performance of sequential tests by studying the stopping-time behavior, showing a considerable advantage over currently-used strategies based on a fixed predetermined measurement time. △ Less

Submitted 14 March, 2024; v1 submitted 27 July, 2023; originally announced July 2023.

Comments: 30 pages, 9 figures

Journal ref: Quantum 8, 1289 (2024)

Low-ground/High ground capacity regions analysis for Bosonic Gaussian Channels

Authors: Farzad Kianvash, Marco Fanizza, Vittorio Giovannetti

Abstract: We present a comprehensive characterization of the interconnections between single-mode, phaseinsensitive Gaussian Bosonic Channels resulting from channel concatenation. This characterization enables us to identify, in the parameter space of these maps, two distinct regions: low-ground and high-ground. In the low-ground region, the information capacities are smaller than a designated reference val… ▽ More We present a comprehensive characterization of the interconnections between single-mode, phaseinsensitive Gaussian Bosonic Channels resulting from channel concatenation. This characterization enables us to identify, in the parameter space of these maps, two distinct regions: low-ground and high-ground. In the low-ground region, the information capacities are smaller than a designated reference value, while in the high-ground region, they are provably greater. As a direct consequence, we systematically outline an explicit set of upper bounds for the quantum and private capacity of these maps, which combine known upper bounds and composition rules, improving upon existing results. △ Less

Submitted 28 June, 2023; originally announced June 2023.

Comments: 18 pages; 7 figures

Quantum soft-covering lemma with applications to rate-distortion coding, resolvability and identification via quantum channels

Authors: Touheed Anwar Atif, S. Sandeep Pradhan, Andreas Winter

Abstract: We propose a quantum soft-covering problem for a given general quantum channel and one of its output states, which consists in finding the minimum rank of an input state needed to approximate the given channel output. We then prove a one-shot quantum covering lemma in terms of smooth min-entropies by leveraging decoupling techniques from quantum Shannon theory. This covering result is shown to be… ▽ More We propose a quantum soft-covering problem for a given general quantum channel and one of its output states, which consists in finding the minimum rank of an input state needed to approximate the given channel output. We then prove a one-shot quantum covering lemma in terms of smooth min-entropies by leveraging decoupling techniques from quantum Shannon theory. This covering result is shown to be equivalent to a coding theorem for rate distortion under a posterior (reverse) channel distortion criterion [Atif, Sohail, Pradhan, arXiv:2302.00625]. Both one-shot results directly yield corollaries about the i.i.d. asymptotics, in terms of the coherent information of the channel. The power of our quantum covering lemma is demonstrated by two additional applications: first, we formulate a quantum channel resolvability problem, and provide one-shot as well as asymptotic upper and lower bounds. Secondly, we provide new upper bounds on the unrestricted and simultaneous identification capacities of quantum channels, in particular separating for the first time the simultaneous identification capacity from the unrestricted one, proving a long-standing conjecture of the last author. △ Less

Submitted 25 July, 2023; v1 submitted 21 June, 2023; originally announced June 2023.

Comments: 29 pages, 3 figures; v2 fixes an error in Definition 6.1 and various typos and minor issues throughout

Floquet time-crystals as sensors of AC fields

Authors: Fernando Iemini, Rosario Fazio, Anna Sanpera

Abstract: We discuss the performance of discrete time crystals (DTCs) as quantum sensors. The long-range spatial and time ordering displayed by DTCs, leads to an exponentially slow heating, turning DTC into advantageous sensors. Specifically, their performance (determined by the quantum Fisher information) to estimate AC fields can overcome the shot-noise limit while allowing for extremely long time sensing… ▽ More We discuss the performance of discrete time crystals (DTCs) as quantum sensors. The long-range spatial and time ordering displayed by DTCs, leads to an exponentially slow heating, turning DTC into advantageous sensors. Specifically, their performance (determined by the quantum Fisher information) to estimate AC fields can overcome the shot-noise limit while allowing for extremely long time sensing protocols. Since the collective response of the many-body interactions stabilizes the DTC dynamics against noise, these sensors become moreover robust to imperfections in the protocol. The performance of such a sensor can also be used in a dual role to probe the presence or absence of a many-body localized phase. △ Less

Submitted 16 October, 2023; v1 submitted 6 June, 2023; originally announced June 2023.

Comments: 6 + 6 pages, 4 + 6 figures

Decoupling by local random unitaries without simultaneous smoothing, and applications to multi-user quantum information tasks

Authors: Pau Colomer, Andreas Winter

Abstract: We show that a simple telescoping sum trick, together with the triangle inequality and a tensorisation property of expected-contractive coefficients of random channels, allow us to achieve general simultaneous decoupling for multiple users via local actions. Employing both old [Dupuis et al. Commun. Math. Phys. 328:251-284 (2014)] and new methods [Dupuis, arXiv:2105.05342], we obtain bounds on the… ▽ More We show that a simple telescoping sum trick, together with the triangle inequality and a tensorisation property of expected-contractive coefficients of random channels, allow us to achieve general simultaneous decoupling for multiple users via local actions. Employing both old [Dupuis et al. Commun. Math. Phys. 328:251-284 (2014)] and new methods [Dupuis, arXiv:2105.05342], we obtain bounds on the expected deviation from ideal decoupling either in the one-shot setting in terms of smooth min-entropies, or the finite block length setting in terms of Rényi entropies. These bounds are essentially optimal without the need to address the simultaneous smoothing conjecture, which remains unresolved. This leads to one-shot, finite block length, and asymptotic achievability results for several tasks in quantum Shannon theory, including local randomness extraction of multiple parties, multi-party assisted entanglement concentration, multi-party quantum state merging, and quantum coding for the quantum multiple access channel. Because of the one-shot nature of our protocols, we obtain achievability results without the need for time-sharing, which at the same time leads to easy proofs of the asymptotic coding theorems. We show that our one-shot decoupling bounds furthermore yield achievable rates (so far only conjectured) for all four tasks in compound settings, that is for only partially known i.i.d. source or channel, which are furthermore optimal for entanglement of assistance and state merging. △ Less

Submitted 29 August, 2023; v1 submitted 24 April, 2023; originally announced April 2023.

Comments: This second version includes new results on the achievable rates of multi-party assisted entanglement distillation and entanglement of assistance in the compound setting, as well as further comments and corrections. The idea of the telescoping trick has independently and concurrently been discovered for multipartite decoupling by Hao-Chung Cheng, Li Gao and Mario Berta. 37 pages, 6 figures

Everything Everywhere All At Once: A First Principles Numerical Demonstration of Emergent Decoherent Histories

Authors: Philipp Strasberg, Teresa E. Reinhard, Joseph Schindler

Abstract: Within the histories formalism the decoherence functional is a formal tool to investigate the emergence of classicality in isolated quantum systems, yet an explicit evaluation of it from first principles has not been reported. We provide such an evaluation for up to five-time histories based on exact numerical diagonalization of the Schroedinger equation. We find a robust emergence of decoherence… ▽ More Within the histories formalism the decoherence functional is a formal tool to investigate the emergence of classicality in isolated quantum systems, yet an explicit evaluation of it from first principles has not been reported. We provide such an evaluation for up to five-time histories based on exact numerical diagonalization of the Schroedinger equation. We find a robust emergence of decoherence for slow and coarse observables of a generic random matrix model and extract a finite size scaling law by varying the Hilbert space dimension over four orders of magnitude. Specifically, we conjecture and observe an exponential suppression of coherent effects as a function of the particle number of the system. This suggests a solution to the preferred basis problem of the many worlds interpretation (or the set selection problem of the histories formalism) within a minimal theoretical framework -- without relying on environmentally induced decoherence, quantum Darwinism, Markov approximations or ensemble averages. We further discuss the implications of our results for the wave function of the Universe, interpretations of quantum mechanics and the arrow(s) of time. △ Less

Submitted 7 February, 2024; v1 submitted 20 April, 2023; originally announced April 2023.

Comments: 14 pages with 11 figures plus references. Substantially revised presentation and discussion compared to v1 but the same main results

Comparison of confidence regions for quantum state tomography

Authors: Jessica O. de Almeida, Matthias Kleinmann, Gael Sentís

Abstract: The quantum state associated to an unknown experimental preparation procedure can be determined by performing quantum state tomography. If the statistical uncertainty in the data dominates over other experimental errors, then a tomographic reconstruction procedure must express this uncertainty. A rigorous way to accomplish this is via statistical confidence regions in state space. Naturally, the s… ▽ More The quantum state associated to an unknown experimental preparation procedure can be determined by performing quantum state tomography. If the statistical uncertainty in the data dominates over other experimental errors, then a tomographic reconstruction procedure must express this uncertainty. A rigorous way to accomplish this is via statistical confidence regions in state space. Naturally, the size of this region decreases when increasing the number of samples, but it also depends critically on the construction method of the region. We compare recent methods for constructing confidence regions as well as a reference method based on a Gaussian approximation. For the comparison, we propose an operational measure with the finding, that there is a significant difference between methods, but which method is preferable can depend on the details of the state preparation scenario. △ Less

Submitted 14 November, 2023; v1 submitted 13 March, 2023; originally announced March 2023.

Comments: 20 pages, 4 figures

Journal ref: New J. Phys. 25 113018 (2023)

Continuity bounds on observational entropy and measured relative entropies

Authors: Joseph Schindler, Andreas Winter

Abstract: We derive a measurement-independent asymptotic continuity bound on the observational entropy for general POVM measurements, making essential use of its property of bounded concavity. The same insight is used to obtain continuity bounds for other entropic quantities, including the measured relative entropy distance to a convex a set of states under a general set of measurements. As a special case,… ▽ More We derive a measurement-independent asymptotic continuity bound on the observational entropy for general POVM measurements, making essential use of its property of bounded concavity. The same insight is used to obtain continuity bounds for other entropic quantities, including the measured relative entropy distance to a convex a set of states under a general set of measurements. As a special case, we define and study conditional observational entropy, which is an observational entropy in one (measured) subsystem conditioned on the quantum state in another (unmeasured) subsystem. We also study continuity of relative entropy with respect to a jointly applied channel, finding that observational entropy is uniformly continuous as a function of the measurement. But we show by means of an example that this continuity under measurements cannot have the form of a concrete asymptotic bound. △ Less

Submitted 4 September, 2023; v1 submitted 1 February, 2023; originally announced February 2023.

Comments: 16 pages; v2 new Corollary 15 on measurement continuity

Classicality with(out) decoherence: Concepts, relation to Markovianity, and a random matrix theory approach

Authors: Philipp Strasberg

Abstract: Answers to the question how a classical world emerges from underlying quantum physics are revisited, connected and extended as follows. First, three distinct concepts are compared: decoherence in open quantum systems, consistent/decoherent histories and Kolmogorov consistency. Second, the crucial role of quantum Markovianity (defined rigorously) to connect these concepts is established. Third, usi… ▽ More Answers to the question how a classical world emerges from underlying quantum physics are revisited, connected and extended as follows. First, three distinct concepts are compared: decoherence in open quantum systems, consistent/decoherent histories and Kolmogorov consistency. Second, the crucial role of quantum Markovianity (defined rigorously) to connect these concepts is established. Third, using a random matrix theory model, quantum effects are shown to be exponentially suppressed in the measurement statistics of slow and coarse observables despite the presence of large amount of coherences. This is also numerically exemplified, and it highlights the potential and importance of non-integrability and chaos for the emergence of classicality. △ Less

Submitted 28 July, 2023; v1 submitted 6 January, 2023; originally announced January 2023.

Comments: Final version

Journal ref: SciPost Phys. 15, 024 (2023)

Information Carried by a Single Particle in Quantum Multiple-Access Channels

Authors: Xinan Chen, Yujie Zhang, Andreas Winter, Virginia O. Lorenz, Eric Chitambar

Abstract: Non-classical features of quantum systems have the potential to strengthen the way we currently exchange information. In this paper, we explore this enhancement on the most basic level of single particles. To be more precise, we compare how well multi-party information can be transmitted to a single receiver using just one classical or quantum particle. Our approach is based on a multiple-access c… ▽ More Non-classical features of quantum systems have the potential to strengthen the way we currently exchange information. In this paper, we explore this enhancement on the most basic level of single particles. To be more precise, we compare how well multi-party information can be transmitted to a single receiver using just one classical or quantum particle. Our approach is based on a multiple-access communication model in which messages can be encoded into a single particle that is coherently distributed across multiple spatial modes. Theoretically, we derive lower bounds on the accessible information in the quantum setting that strictly separate it from the classical scenario. This separation is found whenever there is more than one sender, and also when there is just a single sender who has a shared phase reference with the receiver. Experimentally, we demonstrate such quantum advantage in single-particle communication by implementing a multi-port interferometer with messages being encoded along the different trajectories. Specifically, we consider a two-sender communication protocol built by a three-port optical interferometer. In this scenario, the rate sum achievable with a classical particle is upper bounded by one bit, while we experimentally observe a rate sum of $1.0152\pm0.0034$ bits in the quantum setup. △ Less

Submitted 30 January, 2023; v1 submitted 6 January, 2023; originally announced January 2023.

Comments: 18+10 pages. Comments welcome

Learning quantum processes without input control

Authors: Marco Fanizza, Yihui Quek, Matteo Rosati

Abstract: We introduce a general statistical learning theory for processes that take as input a classical random variable and output a quantum state. Our setting is motivated by the practical situation in which one desires to learn a quantum process governed by classical parameters that are out of one's control. This framework is applicable, for example, to the study of astronomical phenomena, disordered sy… ▽ More We introduce a general statistical learning theory for processes that take as input a classical random variable and output a quantum state. Our setting is motivated by the practical situation in which one desires to learn a quantum process governed by classical parameters that are out of one's control. This framework is applicable, for example, to the study of astronomical phenomena, disordered systems and biological processes not controlled by the observer. We provide an algorithm for learning with high probability in this setting with a finite amount of samples, even if the concept class is infinite. To do this, we review and adapt existing algorithms for shadow tomography and hypothesis selection, and combine their guarantees with the uniform convergence on the data of the loss functions of interest. As a by-product we obtain sufficient conditions for performing shadow tomography of classical-quantum states with a number of copies which depends on the dimension of the quantum register, but not on the dimension of the classical one. We give concrete examples of processes that can be learned in this manner, based on quantum circuits or physically motivated classes, such as systems governed by Hamiltonians with random perturbations or data-dependent phase-shifts. △ Less

Submitted 5 March, 2024; v1 submitted 9 November, 2022; originally announced November 2022.

Comments: 46 pages, 2 figures. v3: New section about technical overview of the learning algorithms added in the introduction. Overall presentation improved, typos corrected

Linear maps as sufficient criteria for entanglement depth and compatibility in many-body systems

Authors: Maciej Lewenstein, Guillem Müller-Rigat, Jordi Tura, Anna Sanpera

Abstract: Physical transformations are described by linear maps that are completely positive and trace preserving (CPTP). However, maps that are positive (P) but not completely positive (CP) are instrumental to derive separability/entanglement criteria. Moreover, the properties of such maps can be linked to entanglement properties of the states they detect. Here, we extend the results presented in [Phys. Re… ▽ More Physical transformations are described by linear maps that are completely positive and trace preserving (CPTP). However, maps that are positive (P) but not completely positive (CP) are instrumental to derive separability/entanglement criteria. Moreover, the properties of such maps can be linked to entanglement properties of the states they detect. Here, we extend the results presented in [Phys. Rev A 93, 042335 (2016)], where sufficient separability criteria for bipartite systems were derived. In particular, we analyze the entanglement depth of an $N$-qubit system by proposing linear maps that, when applied to any state, result in a bi-separable state for the $1:(N-1)$ partitions, i.e., $(N-1)$-entanglement depth. Furthermore, we derive criteria to detect arbitrary $(N-n)$-entanglement depth tailored to states in close vicinity of the completely depolarized state (the normalized identity matrix). We also provide separability (or $1$- entanglement depth) conditions in the symmetric sector, including for diagonal states. Finally, we suggest how similar map techniques can be used to derive sufficient conditions for a set of expectation values to be compatible with separable states or local-hidden-variable theories. We dedicate this paper to the memory of the late Andrzej Kossakowski, our spiritual and intellectual mentor in the field of linear maps. △ Less

Submitted 8 January, 2023; v1 submitted 5 November, 2022; originally announced November 2022.

Comments: 11 pages. Final version

Journal ref: Open Systems & Information Dynamics Vol. 29, No. 03, 2250011 (2022)

Universal algorithms for quantum data learning

Authors: Marco Fanizza, Michalis Skotiniotis, John Calsamiglia, Ramon Muñoz-Tapia, Gael Sentís

Abstract: Operating quantum sensors and quantum computers would make data in the form of quantum states available for purely quantum processing, opening new avenues for studying physical processes and certifying quantum technologies. In this Perspective, we review a line of works dealing with measurements that reveal structural properties of quantum datasets given in the form of product states. These algori… ▽ More Operating quantum sensors and quantum computers would make data in the form of quantum states available for purely quantum processing, opening new avenues for studying physical processes and certifying quantum technologies. In this Perspective, we review a line of works dealing with measurements that reveal structural properties of quantum datasets given in the form of product states. These algorithms are universal, meaning that their performances do not depend on the reference frame in which the dataset is provided. Requiring the universality property implies a characterization of optimal measurements via group representation theory. △ Less

Submitted 21 October, 2022; originally announced October 2022.

Journal ref: Europhysics Letters (2022)

Quantum theory in finite dimension cannot explain every general process with finite memory

Authors: Marco Fanizza, Josep Lumbreras, Andreas Winter

Abstract: Arguably, the largest class of stochastic processes generated by means of a finite memory consists of those that are sequences of observations produced by sequential measurements in a suitable generalized probabilistic theory (GPT). These are constructed from a finite-dimensional memory evolving under a set of possible linear maps, and with probabilities of outcomes determined by linear functions… ▽ More Arguably, the largest class of stochastic processes generated by means of a finite memory consists of those that are sequences of observations produced by sequential measurements in a suitable generalized probabilistic theory (GPT). These are constructed from a finite-dimensional memory evolving under a set of possible linear maps, and with probabilities of outcomes determined by linear functions of the memory state. Examples of such models are given by classical hidden Markov processes, where the memory state is a probability distribution, and at each step it evolves according to a non-negative matrix, and hidden quantum Markov processes, where the memory state is a finite dimensional quantum state, and at each step it evolves according to a completely positive map. Here we show that the set of processes admitting a finite-dimensional explanation do not need to be explainable in terms of either classical probability or quantum mechanics. To wit, we exhibit families of processes that have a finite-dimensional explanation, defined manifestly by the dynamics of explicitly given GPT, but that do not admit a quantum, and therefore not even classical, explanation in finite dimension. Furthermore, we present a family of quantum processes on qubits and qutrits that do not admit a classical finite-dimensional realization, which includes examples introduced earlier by Fox, Rubin, Dharmadikari and Nadkarni as functions of infinite dimensional Markov chains, and lower bound the size of the memory of a classical model realizing a noisy version of the qubit processes. △ Less

Submitted 5 May, 2023; v1 submitted 22 September, 2022; originally announced September 2022.

Comments: 19 pages, added 2 figures

Classicality, Markovianity and local detailed balance from pure state dynamics

Authors: Philipp Strasberg, Andreas Winter, Jochen Gemmer, Jiaozi Wang

Abstract: When describing the effective dynamics of an observable in a many-body system, the repeated randomness assumption, which states that the system returns in a short time to a maximum entropy state, is a crucial hypothesis to guarantee that the effective dynamics is classical, Markovian and obeys local detailed balance. While the latter behaviour is frequently observed in naturally occurring processe… ▽ More When describing the effective dynamics of an observable in a many-body system, the repeated randomness assumption, which states that the system returns in a short time to a maximum entropy state, is a crucial hypothesis to guarantee that the effective dynamics is classical, Markovian and obeys local detailed balance. While the latter behaviour is frequently observed in naturally occurring processes, the repeated randomness assumption is in blatant contradiction to the microscopic reversibility of the system. Here, we show that the use of the repeated randomness assumption can be justified in the description of the effective dynamics of an observable that is both slow and coarse, two properties we will define rigorously. Then, our derivation will invoke essentially only the eigenstate thermalization hypothesis and typicality arguments. While the assumption of a slow observable is subtle, as it provides only a necessary but not sufficient condition, it also offers a unifying perspective applicable to, e.g., open systems as well as collective observables of many-body systems. All our ideas are numerically verified by studying density waves in spin chains. △ Less

Submitted 28 July, 2023; v1 submitted 16 September, 2022; originally announced September 2022.

Comments: Final version

Ultimate limits for quickest quantum change-point detection

Authors: Marco Fanizza, Christoph Hirche, John Calsamiglia

Abstract: Detecting abrupt changes in data streams is crucial because they are often triggered by events that have important consequences if left unattended. Quickest change point detection has become a vital sequential analysis primitive that aims at designing procedures that minimize the expected detection delay of a change subject to a bounded expected false alarm time. We put forward the quantum counter… ▽ More Detecting abrupt changes in data streams is crucial because they are often triggered by events that have important consequences if left unattended. Quickest change point detection has become a vital sequential analysis primitive that aims at designing procedures that minimize the expected detection delay of a change subject to a bounded expected false alarm time. We put forward the quantum counterpart of this fundamental primitive on streams of quantum data. We give a lower-bound on the mean minimum delay when the expected time of a false alarm is asymptotically large, under the most general quantum detection strategy, which is given by a sequence of adaptive collective (potentially weak) measurements on the growing string of quantum data. In addition, we give particular strategies based on repeated measurements on independent blocks of samples, that asymptotically attain the lower-bound, and thereby establish the ultimate quantum limit for quickest change point detection. Finally, we discuss online change point detection in quantum channels. △ Less

Submitted 20 October, 2023; v1 submitted 5 August, 2022; originally announced August 2022.

Comments: 17 pages, 2 figures, close to published version

Phase estimation with limited coherence

Authors: D. Munoz-Lahoz, J. Calsamiglia, J. A. Bergou, E. Bagan

Abstract: We investigate the ultimate precision limits for quantum phase estimation in terms of the coherence, $C$, of the probe. For pure states, we give the minimum estimation variance attainable, $V(C)$, and the optimal state, in the asymptotic limit when the probe system size, $n$, is large. We prove that pure states are optimal only if $C$ scales as $n$ with a sufficiently large proportionality factor,… ▽ More We investigate the ultimate precision limits for quantum phase estimation in terms of the coherence, $C$, of the probe. For pure states, we give the minimum estimation variance attainable, $V(C)$, and the optimal state, in the asymptotic limit when the probe system size, $n$, is large. We prove that pure states are optimal only if $C$ scales as $n$ with a sufficiently large proportionality factor, and that the rank of the optimal state increases with decreasing $C$, eventually becoming full-rank. We show that the variance exhibits a Heisenberg-like scaling, $V(C) \sim a_n/C^2$, where $a_n$ decreases to $π^2/3$ as $n$ increases, leading to a dimension-independent relation. △ Less

Submitted 12 July, 2022; originally announced July 2022.

Comments: 10 pages, 5 figures

Reinforcement-learning calibration of coherent-state receivers on variable-loss optical channels

Authors: Matias Bilkis, Matteo Rosati, John Calsamiglia

Abstract: We study the problem of calibrating a quantum receiver for optical coherent states when transmitted on a quantum optical channel with variable transmissivity, a common model for long-distance optical-fiber and free/deep-space optical communication. We optimize the error probability of legacy adaptive receivers, such as Kennedy's and Dolinar's, on average with respect to the channel transmissivity… ▽ More We study the problem of calibrating a quantum receiver for optical coherent states when transmitted on a quantum optical channel with variable transmissivity, a common model for long-distance optical-fiber and free/deep-space optical communication. We optimize the error probability of legacy adaptive receivers, such as Kennedy's and Dolinar's, on average with respect to the channel transmissivity distribution. We then compare our results with the ultimate error probability attainable by a general quantum device, computing the Helstrom bound for mixtures of coherent-state hypotheses, for the first time to our knowledge, and with homodyne measurements. With these tools, we first analyze the simplest case of two different transmissivity values; we find that the strategies adopted by adaptive receivers exhibit strikingly new features as the difference between the two transmissivities increases. Finally, we employ a recently introduced library of shallow reinforcement learning methods, demonstrating that an intelligent agent can learn the optimal receiver setup from scratch by training on repeated communication episodes on the channel with variable transmissivity and receiving rewards if the coherent-state message is correctly identified. △ Less

Submitted 18 March, 2022; originally announced March 2022.

Comments: 6 pages; 2 figure; presented at 2021 IEEE Information Theory Workshop

Robustness of non-locality in many-body open quantum systems

Authors: Carlo Marconi, Andreu Riera-Campeny, Anna Sanpera, Albert Aloy

Abstract: Non-locality consists in the existence of non-classical correlations between local measurements. So far, it has been investigated mostly in isolated quantum systems. Here we show that non-local correlations are present, can be detected and might be robust against noise also in many-body open quantum systems, both in the steady-state and in the transient regime. We further discuss the robustness of… ▽ More Non-locality consists in the existence of non-classical correlations between local measurements. So far, it has been investigated mostly in isolated quantum systems. Here we show that non-local correlations are present, can be detected and might be robust against noise also in many-body open quantum systems, both in the steady-state and in the transient regime. We further discuss the robustness of non-local correlations when the open quantum system undergoes repeated measurements, a relevant scenario for quantum cryptography. △ Less

Submitted 31 August, 2022; v1 submitted 24 February, 2022; originally announced February 2022.

Characterizing generalized axisymmetric quantum states in $d\times d$ systems

Authors: Marcel Seelbach Benkner, Jens Siewert, Otfried Gühne, Gael Sentís

Abstract: We introduce a family of highly symmetric bipartite quantum states in arbitrary dimensions. It consists of all states that are invariant under local phase rotations and local cyclic permutations of the basis. We solve the separability problem for a subspace of these states and show that a sizable part of the family is bound entangled. We also calculate some of the Schmidt numbers for the family in… ▽ More We introduce a family of highly symmetric bipartite quantum states in arbitrary dimensions. It consists of all states that are invariant under local phase rotations and local cyclic permutations of the basis. We solve the separability problem for a subspace of these states and show that a sizable part of the family is bound entangled. We also calculate some of the Schmidt numbers for the family in $d = 3$, thereby characterizing the dimensionality of entanglement. Our results allow us to estimate entanglement properties of arbitrary states, as general states can be symmetrized to the considered family by local operations. △ Less

Submitted 2 September, 2022; v1 submitted 22 February, 2022; originally announced February 2022.

Comments: 15 pages, 5 figures. Comments are welcome!

Singleton Bounds for Entanglement-Assisted Classical and Quantum Error Correcting Codes

Authors: Manideep Mamindlapally, Andreas Winter

Abstract: We show that entirely quantum Shannon theoretic methods, based on von Neumann entropies and their properties, can be used to derive Singleton bounds on the performance of entanglement-assisted hybrid classical-quantum (EACQ) error correcting codes. Concretely, we show that the triple-rate region of qubits, cbits and ebits of possible EACQ codes over arbitrary alphabet sizes is contained in the qua… ▽ More We show that entirely quantum Shannon theoretic methods, based on von Neumann entropies and their properties, can be used to derive Singleton bounds on the performance of entanglement-assisted hybrid classical-quantum (EACQ) error correcting codes. Concretely, we show that the triple-rate region of qubits, cbits and ebits of possible EACQ codes over arbitrary alphabet sizes is contained in the quantum Shannon theoretic rate region of an associated memoryless erasure channel, which turns out to be a polytope. We show that a large part of this region is attainable by certain EACQ codes, whenever the local alphabet size (i.e. Hilbert space dimension) is large enough, in keeping with known facts about classical and quantum minimum distance separable (MDS) codes: in particular, all of its extreme points and all but one of its extremal lines. The attainability of the remaining one extremal line segment is left as an open question. △ Less

Submitted 19 March, 2023; v1 submitted 4 February, 2022; originally announced February 2022.

Comments: 18 pages, 1 figure; v2 has more details, more references, and self-contained proofs; in v3 some typos are fixed and ORCIDs added; v4 greatly expanded to 22 pages with more references, now 4 figures, improvements to the presentation

A Rate-Distortion Perspective on Quantum State Redistribution

Authors: Zahra Baghali Khanian, Andreas Winter

Abstract: We consider a rate-distortion version of the quantum state redistribution task, where the error of the decoded state is judged via an additive distortion measure; it thus constitutes a quantum generalisation of the classical Wyner-Ziv problem. The quantum source is described by a tripartite pure state shared between Alice ($A$, encoder), Bob ($B$, decoder) and a reference ($R$). Both Alice and Bob… ▽ More We consider a rate-distortion version of the quantum state redistribution task, where the error of the decoded state is judged via an additive distortion measure; it thus constitutes a quantum generalisation of the classical Wyner-Ziv problem. The quantum source is described by a tripartite pure state shared between Alice ($A$, encoder), Bob ($B$, decoder) and a reference ($R$). Both Alice and Bob are required to output a system ($\widetilde{A}$ and $\widetilde{B}$, respectively), and the distortion measure is encoded in an observable on $\widetilde{A}\widetilde{B}R$. It includes as special cases most quantum rate-distortion problems considered in the past, and in particular quantum data compression with the fidelity measured per copy; furthermore, it generalises the well-known state merging and quantum state redistribution tasks for a pure state source, with per-copy fidelity, and a variant recently considered by us, where the source is an ensemble of pure states [1], [2]. We derive a single-letter formula for the rate-distortion function of compression schemes assisted by free entanglement. A peculiarity of the formula is that in general it requires optimisation over an unbounded auxiliary register, so the rate-distortion function is not readily computable from our result, and there is a continuity issue at zero distortion. However, we show how to overcome these difficulties in certain situations. △ Less

Submitted 22 December, 2021; originally announced December 2021.

The role of coherence theory in attractor quantum neural networks

Authors: Carlo Marconi, Pau Colomer Saus, María García Díaz, Anna Sanpera

Abstract: We investigate attractor quantum neural networks (aQNNs) within the framework of coherence theory. We show that: i) aQNNs are associated to non-coherence-generating quantum channels; ii) the depth of the network is given by the decohering power of the corresponding quantum map; and iii) the attractor associated to an arbitrary input state is the one minimizing their relative entropy. Further, we e… ▽ More We investigate attractor quantum neural networks (aQNNs) within the framework of coherence theory. We show that: i) aQNNs are associated to non-coherence-generating quantum channels; ii) the depth of the network is given by the decohering power of the corresponding quantum map; and iii) the attractor associated to an arbitrary input state is the one minimizing their relative entropy. Further, we examine faulty aQNNs described by noisy quantum channels, derive their physical implementation and analyze under which conditions their performance can be enhanced by using entanglement or coherence as external resources. △ Less

Submitted 31 August, 2022; v1 submitted 20 December, 2021; originally announced December 2021.

Journal ref: Quantum 6, 794 (2022)

An approach to $p$-adic qubits from irreducible representations of $SO(3)_p$

Authors: Ilaria Svampa, Stefano Mancini, Andreas Winter

Abstract: We introduce the notion of $p$-adic quantum bit ($p$-qubit) in the context of the $p$-adic quantum mechanics initiated and developed by Volovich and his followers. In this approach, physics takes place in three-dimensional $p$-adic space rather than Euclidean space. Based on our prior work describing the $p$-adic special orthogonal group, we outline a programme to classify its continuous unitary p… ▽ More We introduce the notion of $p$-adic quantum bit ($p$-qubit) in the context of the $p$-adic quantum mechanics initiated and developed by Volovich and his followers. In this approach, physics takes place in three-dimensional $p$-adic space rather than Euclidean space. Based on our prior work describing the $p$-adic special orthogonal group, we outline a programme to classify its continuous unitary projective representations, which can be interpreted as a theory of $p$-adic angular momentum. The $p$-adic quantum bit arises from the irreducible representations of minimal nontrivial dimension two, of which we construct examples for all primes $p$. △ Less

Submitted 13 July, 2022; v1 submitted 6 December, 2021; originally announced December 2021.

Comments: 42 pages

Journal ref: J. Math. Phys. 63, 072202 (2022)

Equilibration of Multitime Quantum Processes in Finite Time Intervals

Authors: Neil Dowling, Pedro Figueroa-Romero, Felix A. Pollock, Philipp Strasberg, Kavan Modi

Abstract: A generic non-integrable (unitary) out-of-equilibrium quantum process, when interrogated across many times, is shown to yield the same statistics as an (non-unitary) equilibrated process. In particular, using the tools of quantum stochastic processes, we prove that under loose assumptions, quantum processes equilibrate within finite time intervals. Sufficient conditions for this to occur are that… ▽ More A generic non-integrable (unitary) out-of-equilibrium quantum process, when interrogated across many times, is shown to yield the same statistics as an (non-unitary) equilibrated process. In particular, using the tools of quantum stochastic processes, we prove that under loose assumptions, quantum processes equilibrate within finite time intervals. Sufficient conditions for this to occur are that multitime observables are coarse grained in both space and time, and that the initial state overlaps with many different energy eigenstates. These results help bridge the gap between (unitary) quantum and (non-unitary) statistical physics, i.e., when all multitime properties and correlations are well approximated by stationary quantities, which includes non-Markovianity and temporal entanglement. We discuss implications of this result for the emergence of classical stochastic processes from multitime measurements of an underlying genuinely quantum system. △ Less

Submitted 16 March, 2023; v1 submitted 2 December, 2021; originally announced December 2021.

Comments: 12+6 pages, 3 figures

Journal ref: SciPost Phys. Core 6, 043 (2023)

Volumes of parent Hamiltonians for benchmarking quantum simulators

Authors: María García Díaz, Gael Sentís, Ramon Muñoz-Tapia, Anna Sanpera

Abstract: We investigate the relative volume of parent Hamiltonians having a target ground state up to some fixed error $ε$, a quantity which sets a benchmark on the performance of quantum simulators. For vanishing error, this relative volume is of measure zero, whereas for a generic $ε$ we show that it increases with the dimension of the Hilbert space. We also address the volume of parent Hamiltonians when… ▽ More We investigate the relative volume of parent Hamiltonians having a target ground state up to some fixed error $ε$, a quantity which sets a benchmark on the performance of quantum simulators. For vanishing error, this relative volume is of measure zero, whereas for a generic $ε$ we show that it increases with the dimension of the Hilbert space. We also address the volume of parent Hamiltonians when they are restricted to be local. For translationally invariant Hamiltonians, we provide an upper bound to their relative volume. Finally, we estimate numerically the relative volume of parent Hamiltonians when the target state is the ground state of the Ising chain in a transverse field. △ Less

Submitted 22 June, 2022; v1 submitted 26 November, 2021; originally announced November 2021.

Comments: published version

Topologically-driven impossibility of superposing unknown states

Authors: Zuzana Gavorová

Abstract: Impossibilities that are unique to quantum mechanics, such as cloning, can deepen our physics understanding and lead to numerous applications. One of the most elementary classical operations is the addition of bit strings. As its quantum version we can take the task of creating a superposition $αe^{iφ(\left|u\right>,\left|v\right>)} \left|u\right>+β\left|v\right>$ from two unknown states… ▽ More Impossibilities that are unique to quantum mechanics, such as cloning, can deepen our physics understanding and lead to numerous applications. One of the most elementary classical operations is the addition of bit strings. As its quantum version we can take the task of creating a superposition $αe^{iφ(\left|u\right>,\left|v\right>)} \left|u\right>+β\left|v\right>$ from two unknown states $\left|u\right>,\left|v\right>\in\mathcal{H}$, where $φ$ is some real function and $α,β\in\mathbb{C}\setminus\{0\}$. Oszmaniec, Grudka, Horodecki and W{ó}jcik [Phys. Rev. Lett. 116(11):110403, 2016] showed that a quantum circuit cannot create a superposition from a single copy of each state. But how many input copies suffice? Due to quantum tomography, the sample complexity seems at most exponential. Surprisingly, we prove that quantum circuits of any sample complexity cannot output a superposition for all input state-pairs $\left|u\right>,\left|v\right>\in\mathcal{H}$ - not even when postselection and approximations are allowed. We show explicitly the limitation on state tomography that precludes its use for superposition. Our result is an application of the topological "lower bound" method [arXiv:2011.10031], which matches any quantum circuit to a continuous function. We find topological arguments showing that no continuous function can output a superposition. This new use of the method offers further understanding of its applicability. Considering state tomography we suggest circumventing our impossibility by relaxing to random superposition or entangled superposition. Random superposition reveals a separation between two types of measurement. Entangled superposition could still be useful as a subroutine. However, both relaxations are inspired by the inefficient state tomography. Whether efficient implementations exist remains open. △ Less

Submitted 18 April, 2022; v1 submitted 3 November, 2021; originally announced November 2021.

Comments: 10 pages, 4 figures, + 7 pages appendices. Rewritten, with an added result on state tomography

Thermality versus objectivity: can they peacefully coexist?

Authors: Thao P. Le, Andreas Winter, Gerardo Adesso

Abstract: Under the influence of external environments, quantum systems can undergo various different processes, including decoherence and equilibration. We observe that macroscopic objects are both objective and thermal, thus leading to the expectation that both objectivity and thermalisation can peacefully coexist on the quantum regime too. Crucially, however, objectivity relies on distributed classical i… ▽ More Under the influence of external environments, quantum systems can undergo various different processes, including decoherence and equilibration. We observe that macroscopic objects are both objective and thermal, thus leading to the expectation that both objectivity and thermalisation can peacefully coexist on the quantum regime too. Crucially, however, objectivity relies on distributed classical information that could conflict with thermalisation. Here, we examine the overlap between thermal and objective states. We find that in general, one cannot exist when the other is present. However, there are certain regimes where thermality and objectivity are more likely to coexist: in the high temperature limit, at the non-degenerate low temperature limit, and when the environment is large. This is consistent with our experiences that everyday-sized objects can be both thermal and objective. △ Less

Submitted 14 November, 2021; v1 submitted 27 September, 2021; originally announced September 2021.

Comments: Published version: 17 + 3 pages, 4 figures, 1 table

Journal ref: Entropy 2021, 23(11), 1506

Relaxation of Multitime Statistics in Quantum Systems

Authors: Neil Dowling, Pedro Figueroa-Romero, Felix A. Pollock, Philipp Strasberg, Kavan Modi

Abstract: Equilibrium statistical mechanics provides powerful tools to understand physics at the macroscale. Yet, the question remains how this can be justified based on a microscopic quantum description. Here, we extend the ideas of pure state quantum statistical mechanics, which focus on single time statistics, to show the equilibration of isolated quantum processes. Namely, we show that most multitime ob… ▽ More Equilibrium statistical mechanics provides powerful tools to understand physics at the macroscale. Yet, the question remains how this can be justified based on a microscopic quantum description. Here, we extend the ideas of pure state quantum statistical mechanics, which focus on single time statistics, to show the equilibration of isolated quantum processes. Namely, we show that most multitime observables for sufficiently large times cannot distinguish a nonequilibrium process from an equilibrium one, unless the system is probed for an extremely large number of times or the observable is particularly fine-grained. A corollary of our results is that the size of non-Markovianity and other multitime characteristics of a nonequilibrium process also equilibrate. △ Less

Submitted 26 May, 2023; v1 submitted 16 August, 2021; originally announced August 2021.

Comments: 7+13 pages, 2+2 figures

Journal ref: Quantum 7, 1027 (2023)

Extendibility limits the performance of quantum processors

Authors: Eneet Kaur, Siddhartha Das, Mark M. Wilde, Andreas Winter

Abstract: Resource theories in quantum information science are helpful for the study and quantification of the performance of information-processing tasks that involve quantum systems. These resource theories also find applications in other areas of study; e.g., the resource theories of entanglement and coherence have found use and implications in the study of quantum thermodynamics and memory effects in qu… ▽ More Resource theories in quantum information science are helpful for the study and quantification of the performance of information-processing tasks that involve quantum systems. These resource theories also find applications in other areas of study; e.g., the resource theories of entanglement and coherence have found use and implications in the study of quantum thermodynamics and memory effects in quantum dynamics. In this paper, we introduce the resource theory of unextendibility, which is associated to the inability of extending quantum entanglement in a given quantum state to multiple parties. The free states in this resource theory are the k-extendible states, and the free channels are k-extendible channels, which preserve the class of k-extendible states. We make use of this resource theory to derive non-asymptotic, upper bounds on the rate at which quantum communication or entanglement preservation is possible by utilizing an arbitrary quantum channel a finite number of times, along with the assistance of k-extendible channels at no cost. We then show that the bounds obtained are significantly tighter than previously known bounds for quantum communication over both the depolarizing and erasure channels. △ Less

Submitted 6 August, 2021; originally announced August 2021.

Comments: 7 pages, 2 figures, see companion paper at arXiv:1803.10710

Journal ref: Physical Review Letters, vol. 123, no. 7, page 070502, August 2019

Open quantum systems coupled to finite baths: A hierarchy of master equations

Authors: Andreu Riera-Campeny, Anna Sanpera, Philipp Strasberg

Abstract: An open quantum system in contact with an infinite bath approaches equilibrium, while the state of the bath remains unchanged. If the bath is finite, the open system still relaxes to equilibrium, but it induces a dynamical evolution of the bath state. In this work, we study the dynamics of open quantum systems in contact with finite baths. We obtain a hierarchy of master equations that improve the… ▽ More An open quantum system in contact with an infinite bath approaches equilibrium, while the state of the bath remains unchanged. If the bath is finite, the open system still relaxes to equilibrium, but it induces a dynamical evolution of the bath state. In this work, we study the dynamics of open quantum systems in contact with finite baths. We obtain a hierarchy of master equations that improve their accuracy by including more dynamical information of the bath. For instance, as the least accurate but simplest description in the hierarchy we obtain the conventional Born-Markov-secular master equation. Remarkably, our framework works even if the measurements of the bath energy are imperfect, which, not only is more realistic, but also unifies the theoretical description. Also, we discuss this formalism in detail for a particular non-interacting environment where the Boltzmann temperature and the Kubo-Martin-Schwinger relation naturally arise. Finally, we apply our hierarchy of master equations to study the central spin model. △ Less

Submitted 19 May, 2022; v1 submitted 4 August, 2021; originally announced August 2021.

Online identification of symmetric pure states

Authors: Gael Sentís, Esteban Martínez-Vargas, Ramon Muñoz-Tapia

Abstract: We consider online strategies for discriminating between symmetric pure states with zero error when $n$ copies of the states are provided. Optimized online strategies involve local, possibly adaptive measurements on each copy and are optimal at each step, which makes them robust in front of particle losses or an abrupt termination of the discrimination process. We first review previous results on… ▽ More We consider online strategies for discriminating between symmetric pure states with zero error when $n$ copies of the states are provided. Optimized online strategies involve local, possibly adaptive measurements on each copy and are optimal at each step, which makes them robust in front of particle losses or an abrupt termination of the discrimination process. We first review previous results on binary minimum and zero error discrimination with local measurements that achieve the maximum success probability set by optimizing over global measurements, highlighting their online features. We then extend these results to the case of zero error identification of three symmetric states with constant overlap. We provide optimal online schemes that attain global performance for any $n$ if the state overlaps are positive, and for odd $n$ if overlaps have a negative value. For arbitrary complex overlaps, we show compelling evidence that online schemes fail to reach optimal global performance. The online schemes that we describe only require to store the last outcome obtained in a classical memory, and adaptiveness of the measurements reduce to at most two changes, regardless of the value of $n$. △ Less

Submitted 30 January, 2022; v1 submitted 5 July, 2021; originally announced July 2021.

Comments: 12 pages, 1 figure

Journal ref: Quantum 6, 658 (2022)