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Physica Scripta

Characterizing nonclassical correlation via local channels

R. Muthuganesan, S. Balakrishnan

Published Jul 19, 2024• 1 citation
Publisher

Abstract

Abstract Local operation is an important tool to characterize the nonlocal aspects of multipartite quantum system. Exploiting the notion of resource theory of coherence, in this article, we establish a quantum correlation measure as the difference between the bipartite coherence and marginal state coherence. We study the Tsallis α-entropy (TαE) coherence based quantum correlation of bipartite state relative to different channels such as unitary channel, the twirling (unitary-induced) channel, projective measurements and weak measurements. It is shown that the quantum channel helps us to discriminate the product and classical-quantum states. We provide the operational interpretation of the correlation measure relative to the measurement in terms of classical uncertainty of channel. A closer connection between the correlation relative to the projective measurements and weak measurements is obtained in terms of measurement strength. As an illustration, we have studied the quantum correlations of well-known two-qubit states.

DOI
10.1088/1402-4896/ad65c7

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Abstract Local operation is an important tool to characterize the nonlocal aspects of multipartite quantum system. Exploiting the notion of resource theory of coherence, in this article, we establish a quantum correlation measure as the difference between the bipartite coherence and marginal state coherence. We study the Tsallis α-entropy (TαE) coherence based quantum correlation of bipartite state relative to different channels such as unitary channel, the twirling (unitary-induced) channel, projective measurements and weak measurements. It is shown that the quantum channel helps us to discriminate the product and classical-quantum states. We provide the operational interpretation of the correlation measure relative to the measurement in terms of classical uncertainty of channel. A closer connection between the correlation relative to the projective measurements and weak measurements is obtained in terms of measurement strength. As an illustration, we have studied the quantum correlations of well-known two-qubit states.
Quantum channels, in general, will disturb quantum states and will lead to decoherence (i.e., information leakage to the environment). For bipartite systems, local channels often cause more decoherence for global states than for local states due to correlations. Intuitively, the difference between these two kinds of decoherence (i.e., global and local ones) may be regarded as a quantifier characterizing certain aspects of correlations in the global bipartite states. Based on this idea, we introduce a quantifier of correlations (relative to a local channel) as the coherence difference and investigate its basic properties. We probe and quantify correlations relative to various channels including the unitary channels, the twirling channels, the projective measurements, and the weak measurements. In particular, we show that both product states and some natural classical-quantum states can be operationally characterized in terms of local channels: The product states are just those states with vanishing coherence difference relative to the twirling channel induced by the unitary group, whereas these natural classical-quantum states are just those states with vanishing coherence difference relative to the twirling channel induced by the subgroup of the unitary group that does not disturb the local states. We further illustrate the results by various examples.
Abstract In this article, we study quantum coherence of bipartite state from the perspective of weak measurement, which generalizes the notion of coherence relative to measurement. This is being illustrated by computing coherence for the well-known Bell diagonal and Werner states. Further, we have expanded the notion of coherence to encompass correlations, exploring its connections with other quantifications of nonlocality. We have determined that this coherence measure can be perceived as a generalized version of the Wigner-Yanese skew information measure and several other nonlocal measures. As a natural extension, we introduce uncertainty relations within the context of weak measurements. Additionally, we propose a novel form of variance by considering the weak value of an observable within a comprehensive framework.
Nonclassical correlations are significant physical resources with extensive applications in quantum information processing. We introduce the modified Wigner-Yanase-Dyson skew information of a quantum state relative to a quantum channel, and a quantitative measure of quantum correlations. Their basic properties are explored in detail. Through a specific example, we also compare our correlations measure with the existing one. Moreover, the correlations relative to various channels including the von Neumann measurements, the unitary channels and the twirling channels are analyzed.
Abstract Quantum coherence characterizes the non-classical feature of a single party system with respect to a local basis. Based on a recently introduced resource framework, coherence can be regarded as a resource and be systematically manipulated and quantified. Operationally, coherence quantifies the intrinsic randomness of the outcome of the projective measurement in the system’s computational basis. However, such a relation is only proven when randomness is characterized by the von Neumann entropy. In this work, we consider several recently proposed coherence measures and relate them to the general uncertainties of the projective measurement outcome conditioned on all the other systems. Our work thus provides a unified framework for redefining several coherence measures via general conditional entropies. Based on the relation, we numerically calculate the coherence measures via semi-definite programming. Furthermore, we discuss the operational meaning of the unified definition. Our result highlights the close relation between single partite coherence and bipartite quantum correlation.
Quantum mechanics is a highly nonlocal theory of nature. Quantum systems exhibit correlations which cannot be described by any classical theory of locality. We develop the resource theory of dynamical Bell nonlocality, which includes bipartite states, classical channels, quantum channels and measurements. In the state scenario, all separable states are Bell local. However, there exist mixed bipartite entangled states which also admit Bell local behaviour. To address this anomaly, we introduce the notion of fully Bell locality and show that all entangled states are Bell nonlocal, in the sense that they can be used to simulate at least one nonlocal bipartite Positive Operator Valued Measure (POVM) channel. We take a step further and generalise this result to bipartite entangled quantum channels. We then generalize the CHSH inequality from bipartite classical channels to bipartite POVM channels and devise a technique to check if a given bipartite POVM channel is nonlocal or not. Finally we provide a systematic method to quantify Bell nonlocality of bipartite quantum channels by extending any monotone for Bell nonlocality of classical channels to quantum channels and also introduce the precise definition of relative entropy of Bell nonlocality. We leave some open problems in the way.