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arXiv:2206.10800 · Physical Review A

Classical and quantum parts of conditional mutual information for open quantum systems

Zhiqiang Huang, Xiao-Kan Guo

Published Oct 10, 2022• 4 citations
arXivHTMLPDF

Abstract

We study the classical, classical-quantum, and quantum parts of conditional mutual information in the ``system-environment-ancilla'' setting of open quantum systems. We perform the separation of conditional mutual information by generalizing the classification of correlations of quantum states. The condition for identifying the classical part of conditional mutual information is given by adapting the no-local-broadcasting theorem to this setting, while the condition for the classical-quantum part of conditional mutual information is obtained by considering the multipartite quantum discord and the no-unilocal-broadcasting theorem. For the quantum part of conditional mutual information, we further generalize the characterization of entanglement by quantum discord of state extensions to the multipartite setting to derive a generalized Koashi-Winter-type monogamy equality for conditional mutual information. Our results have explicit dependence on the extensions of the environment, which are useful for studying different environmental contributions to the quantum non-Markovianity of open quantum systems.

DOI
10.1103/physreva.106.042412

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We study the classical, classical-quantum, and quantum parts of conditional mutual information in the ``system-environment-ancilla'' setting of open quantum systems. We perform the separation of conditional mutual information by generalizing the classification of correlations of quantum states. The condition for identifying the classical part of conditional mutual information is given by adapting the no-local-broadcasting theorem to this setting, while the condition for the classical-quantum part of conditional mutual information is obtained by considering the multipartite quantum discord and the no-unilocal-broadcasting theorem. For the quantum part of conditional mutual information, we further generalize the characterization of entanglement by quantum discord of state extensions to the multipartite setting to derive a generalized Koashi-Winter-type monogamy equality for conditional mutual information. Our results have explicit dependence on the extensions of the environment, which are useful for studying different environmental contributions to the quantum non-Markovianity of open quantum systems.
A generalization of quantum discord to multipartite systems is proposed. A key feature of our formulation is its consistency with the conventional definition of discord in bipartite systems. It is by construction zero only for systems with classically correlated subsystems and is a non-negative quantity, giving a measure of the total nonclassical correlations in the multipartite system with respect to a fixed measurement ordering. For the tripartite case, we show that the discord can be decomposed into contributions resulting from changes induced by nonclassical correlation breaking measurements in the conditional mutual information and tripartite mutual information. The former gives a measure of the bipartite nonclassical correlations and is a non-negative quantity, while the latter is related to the monogamy of the nonclassical correlations.
We discuss the interconnections between basic correlation measures of a bipartite quantum state and basic information characteristics of a quantum channel, focusing on the benefits of these interconnections for solving specific problems concerning the characteristics of both types. We describe properties of the (unoptimized and optimized) quantum discord in infinite-dimensional bipartite systems. In particular, using the generalized Koashi–Winter relation, a simple condition is obtained that guarantees that a state with zero quantum discord is quantum-classical. Two possible definitions of the quantum discord for states with infinite one-way classical correlation are proposed and analysed. The generalized versions of Koashi–Winter and Xi–Lu–Wang–Li relations are used to obtain advanced continuity bounds for the Holevo information at the outputs of a channel and its complementary channel (as functions of a channel for a given ensemble of input states), for the Holevo capacity and the unregularized private capacity of a quantum channel depending either on the input dimension or on the input energy bound. We also discuss the properties of quantum channels which are “doppelgangers” of the monotonicity of the quantum discord and the entropy reduction of a local measurement under quantum channels acting on an unmeasured subsystem.
We provide experimental evidence of quantum features in bipartite states classified as entirely classical according to a conventional criterion based on the Glauber P\mathcal{P}P function but possessing nonzero Gaussian quantum discord. Their quantum nature is experimentally revealed by acting locally on one part of the discordant state. We experimentally verify and investigate the effect of discord increase under the action of local loss and link it to the entanglement with the environment. Adding an environmental system purifying the state, we unveil the flow of quantum correlations within a global pure system using the Koashi-Winter inequality. For a discordant state generated by splitting a state in which the initial squeezing is destroyed by random displacements, we demonstrate the recovery of entanglement highlighting the role of system-environment correlations.
In this paper, we study measures of quantum non-Markovianity based on the conditional mutual information. We obtain such measures by considering multiple parts of the total environment such that the conditional mutual information can be defined in this multipartite setup. The benefit of this approach is that the conditional mutual information is closely related to recovery maps and Markov chains; we also point out its relations with the change in distinguishability. We study along the way the properties of leaked information, which is the conditional mutual information that can be back flowed, and we use this leaked information to show that the correlated environment is necessary for the nonlocal memory effect.
By combining a measure of total correlations, mutual information, and the notion of broadcast —i.e. generally non‐factorized— copies of states of distributed systems, we are able to characterize in a single framework different levels of quantumness of correlations, corresponding to the classification of strictly classical, separable, and entangled states. We find that the broadcast regularization of mutual information —defined as the minimal per‐copy mutual information between parties, when they share an infinite amount of broadcast copies— besides having by construction an appealing interpretation, satisfies many of the properties of an entanglement measure. In particular, it vanishes for separable states while it is strictly positive for all entangled states. The latter fact may be considered a signature of monogamy of entangled correlations.
Abstract. In an initially uncorrelated mixed separable bi-partite system, quantum correlations can emerge under the action of a local measurement or local noise [1]. We analyze this counter-intuitive phenomenon using quantum discord as a quantifier. We then relate changes in quantum discord to system-environment correlations between the system in a mixed state and some purifying environmental mode using the Koashi-Winter inequality. On this basis, we suggest an interpretation of discord as a byproduct of transferring entanglement and correlations around the different subsystems of a global pure state.