Entanglement-breaking Channels Research Articles

Compressing continuous variable quantum measurements

We generalize the notion of joint measurability to continuous variable systems by extending a recently introduced compression algorithm of quantum measurements to this realm. The extension results in a property that asks for the minimal dimensional quantum system required for representing a given set of quantum measurements. To illustrate the concept, we show that the canonical pair of position and momentum is completely incompressible. We translate the concept of measurement compression to the realm of quantum correlations, where it results in a generalization of continuous variable quantum steering. In contrast to the steering scenario, which detects entanglement, the generalization detects the dimensionality of entanglement. We illustrate the bridge between the concepts by showing that an analogue of the original EPR argument is genuinely infinite-dimensional with respect to our figure of merit, and that a fundamental discrete variable result on preparability of unsteerable state assemblages with separable states does not directly carry over to the continuous variable setting. We further prove a representation result for partially entanglement breaking channels that can be of independent interest.

Verification of continuous-variable quantum memories

A proper quantum memory is argued to consist in a quantum channel which cannot be simulated with a measurement followed by classical information storage and a final state preparation, i.e. with an entanglement breaking (EB) channel. The verification of quantum memories (non-EB channels) is a task in which an honest user wants to test the quantum memory of an untrusted, remote provider. This task is inherently suited for the class of protocols with trusted quantum inputs, sometimes called measurement-device-independent (MDI) protocols. Here, we study the MDI certification of non-EB channels in continuous variable (CV) systems. We provide a simple witness based on adversarial metrology, and describe an experimentally friendly protocol that can be used to verify all non Gaussian incompatibility breaking quantum memories. Our results can be tested with current technology and can be applied to test other devices resulting in non-EB channels, such as CV quantum transducers and transmission lines.

Communication over entanglement-breaking channels with unreliable entanglement assistance

Communication over entanglement-breaking channels with unreliable entanglement assistance

The Communication Value of a Quantum Channel

There are various ways to quantify the communication capabilities of a quantum channel. In this work we introduce the communication value (cv) of quantum channel, which describes the optimal probability of guessing the channel input from its output. By connecting to prior work on zero-error channel simulation, we show that the cv and its entanglement-assisted variant also offer dual interpretations as the classical communication cost for perfectly simulating different aspects of a channel using non-signaling resources. Our study involves characterizing the communication value as a generalized conditional min-entropy over the cone of separable operators. Using this characterization, we evaluate the cv for all qubit channels and higher-dimensional channels with certain symmetries. We find that the any entanglement-breaking channel has multiplicative cv when used in parallel with any other channel; the same is shown to hold for Pauli channels and partially depolarizing channels. In contrast, the cv is found to be non-multiplicative for a subset of the well-known Werner-Holevo channels. A final component of this work investigates relaxations of the channel cv to other cones such as the set of operators having a positive partial transpose (PPT).

Bounds on the breaking time for entanglement-breaking channels

Entanglement-breaking channels are quantum channels transforming entangled states to separable states. Despite a detailed discussion of their operational structure, to be found in the literature, studies on dynamical characteristics of this type of maps are yet limited. We consider one of the basic questions: for Lindblad-type dynamics, when does a given channel break entanglement? We discuss the finite-dimensional case where the quantification of entanglement via entanglement witnesses is utilized. For the general setup, we use the method of quantum speed limit to derive lower bounds on entanglement breaking times in terms of an input state, the dynamical map and the witness operator. Then, with a particular choice of the input state and the entanglement witness, the bounds for the breaking time are turned to solely reflect the characteristics of the dynamics.

Communication advantage of quantum compositions of channels from non-Markovianity

The combined use of quantum channels can grant communication advantages in the form of enhancements to communication capacities. One such channel composition is the quantum switch, which implements a system with indefinite causal order by coherent control of the orderings of two or more quantum channels, resulting in enhanced communication capacities. Here, using the monogamy relation, we studied the flow of entanglement monotone in these quantum compositions of channels in the environmental representation. We implemented the two-party quantum switch in this framework, and demonstrated that non-Markovianity is the source of revival of the entanglement monotone in this setup. The possibility and amount of revival was shown to depend on the entangling capability of the channels, and the perfect activation of coherent information with entanglement-breaking channels was also replicated with the perfect revival of entanglement monotone. Additionally, we showed that a more general non-Markovian circuit can still grant enhancements to coherent information and Holevo quantity without the presence of indefinite causal order.

Quantum-machine-learning channel discrimination

In the problem of quantum channel discrimination, one distinguishes between a given number of quantum channels, which is done by sending an input state through a channel and measuring the output state. This work studies applications of variational quantum circuits and machine-learning techniques for discriminating such channels. In particular, we explore (i) the practical implementation of embedding this task into the framework of variational quantum computing, (ii) training a quantum classifier based on variational quantum circuits, and (iii) applying the quantum kernel estimation technique. For testing these three channel discrimination approaches, we considered a pair of entanglement-breaking channels and the depolarizing channel with two different depolarization factors. For the approach (i), we address solving the quantum channel discrimination problem using widely discussed parallel and sequential strategies. We show the advantage of the latter in terms of better convergence with less quantum resources. Quantum channel discrimination with a variational quantum classifier (ii) allows one to operate even with random and mixed input states and simple variational circuits. The kernel-based classification approach (iii) is also found effective as it allows one to discriminate depolarizing channels associated not with just fixed values of the depolarization factor, but with ranges of it. Additionally, we discovered that a simple modification of one of the commonly used kernels significantly increases the efficiency of this approach. Finally, our numerical findings reveal that the performance of variational methods of channel discrimination depends on the trace of the product of the output states. These findings demonstrate that quantum machine learning can be used to discriminate channels, such as those representing physical noise processes.

Usefulness of adaptive strategies in asymptotic quantum channel discrimination

Adaptiveness is a key principle in information processing including statistics and machine learning. We investigate the usefulness adaptive methods in the framework of asymptotic binary hypothesis testing, when each hypothesis represents asymptotically many independent instances of a quantum channel, and the tests are based on using the unknown channel and observing outputs. Unlike the familiar setting of quantum states as hypotheses, there is a fundamental distinction between adaptive and nonadaptive strategies with respect to the channel uses, and we introduce a number of further variants of the discrimination tasks by imposing different restrictions on the test strategies. The following results are obtained: (1) We prove that for classical-quantum channels, adaptive and nonadaptive strategies lead to the same error exponents both in the symmetric (Chernoff) and asymmetric (Hoeffding, Stein) settings. (2) The first separation between adaptive and nonadaptive symmetric hypothesis testing exponents for quantum channels, which we derive from a general lower bound on the error probability for nonadaptive strategies; the concrete example we analyze is a pair of entanglement-breaking channels. (3) We prove, in some sense generalizing the previous statement, that for general channels adaptive strategies restricted to classical feed-forward and product state channel inputs are not superior in the asymptotic limit to nonadaptive product state strategies. (4) As an application of our findings, we address the discrimination power of an arbitrary quantum channel and show that adaptive strategies with classical feedback and no quantum memory at the input do not increase the discrimination power of the channel beyond nonadaptive tensor product input strategies.

Communication Over Quantum Channels With Parameter Estimation

Communication over a random-parameter quantum channel when the decoder is required to reconstruct the parameter sequence is considered. We study scenarios that include either strictly-causal, causal, or non-causal channel side information (CSI) available at the encoder, and also when CSI is not available. This model can be viewed as a form of quantum metrology, and as the quantum counterpart of the classical rate-and-state channel with state estimation at the decoder. Regularized formulas for the capacity-distortion regions are derived. In the special case of measurement channels, single-letter characterizations are derived for the strictly-causal and causal settings. Furthermore, in the more general case of entanglement-breaking channels, a single-letter characterization is derived when CSI is not available. As a consequence, we obtain regularized formulas for the capacity of random-parameter quantum channels with CSI, generalizing previous results by Boche <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i> , 2016, on classical-quantum channels. Bosonic dirty paper coding is introduced as a consequence, where we demonstrate that the optimal coefficient is not necessarily that of minimum mean-square error estimation as in the classical setting.

Operational Characterization of Infinite-Dimensional Quantum Resources.

Recently, various nonclassical properties of quantum states and channels have been characterized through an advantage they provide in quantum information tasks over their classical counterparts. Such advantage can be typically proven to be quantitative, in that larger amounts of quantum resources lead to better performance in the corresponding tasks. So far, these characterizations have been established only in the finite-dimensional setting, hence, leaving out central resources in continuous variable systems such as entanglement and nonclassicality of states as well as entanglement breaking and broadcasting channels. In this Letter, we present a fully general framework for resource quantification in infinite-dimensional systems. The framework is applicable to a wide range of resources with the only premises being that classical randomness cannot create a resource and that the resourceless objects form a closed set in an appropriate sense. As the latter may be hard to establish for the abstract topologies of continuous variable systems, we provide a relaxation of the condition with no reference to topology. This envelopes the aforementioned resources and various others, hence, giving them an interpretation as performance enhancement in so-called input-output games.

Entanglement breaking channels, stochastic matrices, and primitivity

We consider the important class of quantum operations (completely positive trace-preserving maps) called entanglement breaking channels. We show how every such channel induces stochastic matrix representations that have the same non-zero spectrum as the channel. We then use this to investigate when entanglement breaking channels are primitive, and prove this depends on primitivity of the matrix representations. This in turn leads to tight bounds on the primitivity index of entanglement breaking channels in terms of the primitivity index of the associated stochastic matrices. We also present examples and discuss open problems generated by the work.

Random-Receiver Quantum Communication

We introduce the task of random-receiver quantum communication, in which a sender transmits a quantum message to a receiver selected from a list of n spatially separated parties. At the moment of transmission, the choice of receiver is unknown to the sender. Later, it becomes known to the n parties, who coordinate their actions by exchanging classical messages. In normal conditions, random-receiver quantum communication requires a noiseless quantum communication channel between the sender and each of the n receivers. In contrast, we show that random-receiver quantum communication can take place through noisy, entanglement-breaking channels if the order of such channels is coherently controlled by a quantum bit that is accessible through measurements. While this phenomenon is achieved with a single control qubit, it cannot be mimicked by adding a noiseless qubit channel from the sender to any of the receivers, or more generally, from the sender to any subset of k<n parties.Received 19 November 2020Accepted 26 May 2021DOI:https://doi.org/10.1103/PRXQuantum.2.020350Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasQuantum channelsQuantum communicationQuantum correlations in quantum informationQuantum information processingQuantum networksQuantum Information

Information scrambling and chaos in open quantum systems

Out-of-time-ordered correlators (OTOCs) have been extensively used over the last few years to study information scrambling and quantum chaos in many-body systems. In this paper, we extend the formalism of the averaged bipartite OTOC of Styliaris et al [Phys. Rev. Lett. 126, 030601 (2021)] to the case of open quantum systems. The dynamics is no longer unitary but it is described by more general quantum channels (trace preserving, completely positive maps). This "open bipartite OTOC" can be treated in an exact analytical fashion and is shown to amount to a distance between two quantum channels. Moreover, our analytical form unveils competing entropic contributions from information scrambling and environmental decoherence such that the latter can obfuscate the former. To elucidate this subtle interplay we analytically study special classes of quantum channels, namely, dephasing channels, entanglement-breaking channels, and others. Finally, as a physical application we numerically study dissipative many-body spin-chains and show how the competing entropic effects can be used to differentiate between integrable and chaotic regimes.

Jordan products of quantum channels and their compatibility

Given two quantum channels, we examine the task of determining whether they are compatible—meaning that one can perform both channels simultaneously but, in the future, choose exactly one channel whose output is desired (while forfeiting the output of the other channel). Here, we present several results concerning this task. First, we show it is equivalent to the quantum state marginal problem, i.e., every quantum state marginal problem can be recast as the compatibility of two channels, and vice versa. Second, we show that compatible measure-and-prepare channels (i.e., entanglement-breaking channels) do not necessarily have a measure-and-prepare compatibilizing channel. Third, we extend the notion of the Jordan product of matrices to quantum channels and present sufficient conditions for channel compatibility. These Jordan products and their generalizations might be of independent interest. Last, we formulate the different notions of compatibility as semidefinite programs and numerically test when families of partially dephasing-depolarizing channels are compatible.

Nullspaces of entanglement breaking channels and applications

Quantum entanglement breaking channels are a fundamental class of quantum operations; originally investigated for quantum information theoretic reasons, their study has since grown to touch on many aspects of quantum information science. Here we investigate the nullspace structures of entanglement breaking channels and we derive a pair of related applications. We show that every operator space of trace zero matrices is the nullspace of an entanglement breaking channel. We derive a test for mixed unitarity of quantum channels based on complementary channel behaviour and entanglement breaking channel nullspaces. We identify conditions that guarantee the existence of private algebras for certain classes of entanglement breaking channels.

Geometry of symmetric and noninvertible Pauli channels

We analyze the geometry of positive and completely positive, trace-preserving Pauli maps that are fully determined by up to two distinct parameters. This includes five classes of symmetric and noninvertible Pauli channels. Using the Hilbert-Schmidt metric in the space of the Choi-Jamio\l{}kowski states, we compute the relative volumes of entanglement breaking, time-local generated, and divisible channels. Finally, we find the shapes of the complete positivity regions in relation to the tetrahedron of all Pauli channels.

Structure of quantum and classical implementations of the Popescu-Rohrlich box

We construct implementations of the PR-box using quantum and classical channels as state spaces. In both cases our constructions are very similar and they share the same idea taken from general probabilistic theories and the square state space model. We construct all quantum qubit channels that maximally violate a given CHSH inequality, we show that they all are entanglement-breaking channels, that they have certain block-diagonal structure and we present some examples of such channels.

Entanglement-breaking superchannels

In this paper we initiate the study of entanglement-breaking (EB) superchannels. These are processes that always yield separable maps when acting on one side of a bipartite completely positive (CP) map. EB superchannels are a generalization of the well-known EB channels. We give several equivalent characterizations of EB supermaps and superchannels. Unlike its channel counterpart, we find that not every EB superchannel can be implemented as a measure-and-prepare superchannel. We also demonstrate that many EB superchannels can be superactivated, in the sense that they can output non-separable channels when wired in series.We then introduce the notions of CPTP- and CP-complete images of a superchannel, which capture deterministic and probabilistic channel convertibility, respectively. This allows us to characterize the power of EB superchannels for generating CP maps in different scenarios, and it reveals some fundamental differences between channels and superchannels. Finally, we relax the definition of separable channels to include(p,q)-non-entangling channels, which are bipartite channels that cannot generate entanglement usingp- andq-dimensional ancillary systems. By introducing and investigatingk-EB maps, we construct examples of(p,q)-EB superchannels that are not fully entanglement breaking. Partial results on the characterization of(p,q)-EB superchannels are also provided.

The Quantum Illumination Story

Superposition and entanglement, the quintessential characteristics of quantum physics, have been shown to provide communication, computation, and sensing capabilities that go beyond what classical physics will permit. It is natural, therefore, to explore their application to radar, despite the fact that decoherence—caused by the loss and noise encountered in radar sensing—destroys these fragile quantum properties. This article tells the story of “quantum illumination,” an entanglement-based approach to quantum radar, from its inception to its current understanding. Remarkably, despite loss and noise that destroy its initial entanglement, quantum illumination does offer a target-detection performance improvement over a classical radar of the same transmitted energy. A realistic assessment of that improvement's utility, however, shows that its value is severely limited. Nevertheless, the fact that entanglement can be of value on an entanglement-breaking channel—the meta-lesson of the quantum illumination story—should spur continued research on quantum radar.

Entanglement breaking rank and the existence of SIC POVMs

We introduce and study the entanglement breaking rank of an entanglement breaking channel. We show that the entanglement breaking rank of the channel Z:Md→Md defined by Z(X)=1d+1(X+Tr(X)Id) is d2 if and only if there exists a symmetric informationally complete positive operator-valued measure in dimension d.