Entanglement Irreversibility from Quantum Discord and Quantum Deficit

One of the best signatures of nonclassicality in a quantum system is the existence of correlations that have no classical counterpart. Different methods for quantifying the quantum and classical parts of correlations are amongst the more actively-studied topics of quantum information theory over the past decade. Entanglement is the most prominent of these correlations, but in many cases unentangled states exhibit nonclassical behavior too. Thus distinguishing quantum correlations other than entanglement provides a better division between the quantum and classical worlds, especially when considering mixed states. Here we review different notions of classical and quantum correlations quantified by quantum discord and other related measures. In the first half, we review the mathematical properties of the measures of quantum correlations, relate them to each other, and discuss the classical-quantum division that is common among them. In the second half, we show that the measures identify and quantify the deviation from classicality in various quantuminformation-processing tasks, quantum thermodynamics, open-system dynamics, and many-body physics. We show that in many cases quantum correlations indicate an advantage of quantum methods over classical ones.

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“…The same equation is first noted in (Cornelio et al, 2011;Fanchini et al, 2011a) in different contexts (see Secs. V.E and VI.B.3).…”

Section: Entanglement Consumption In State Mergingsupporting

confidence: 62%

The classical-quantum boundary for correlations: Discord and related measures

et al. 2012

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“…Over the past decade, quantum discord has received a lot of attentions in Refs. [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30], and also see the reviews [4,5].…”

Section: Introductionmentioning

confidence: 99%

Necessary and sufficient condition for saturating the upper bound of quantum discord

Wang

et al. 2012

Phys. Rev. A

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We revisit the upper bound of quantum discord given by the von Neumann entropy of the measured subsystem. Using the Koashi-Winter relation, we obtain a trade-off between the amount of classical correlation and quantum discord in the tripartite pure states. The difference between the quantum discord and its upper bound is interpreted as a measure on the classical correlative capacity. Further, we give the explicit characterization of the quantum states saturating the upper bound of quantum discord, through the equality condition for the Araki-Lieb inequality. We also demonstrate that the saturating of the upper bound of quantum discord precludes any further correlation between the measured subsystem and the environment.

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“…It has been shown that it is present in almost all quantum states [14] and the relation between discord and entanglement has been discussed [15][16][17]. In contrast with entanglement, discord can be generated using local noise [18] and it is not monogamous [19].…”

Section: Introductionmentioning

confidence: 99%

Unified view of correlations using the square-norm distance

et al. 2012

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The distance between a quantum state and its closest state not having a certain property has been used to quantify the amount of correlations corresponding to that property. This approach allows a unified view of the various kinds of correlations present in a quantum system. In particular, using relative entropy as a distance measure, total correlations can be meaningfully separated in a quantum and a classical part thanks to an additive relation involving only distances between states. Here, we investigate a unified view of correlations using as distance measure the square norm, already used to define the so-called geometric quantum discord. We thus consider geometric quantifiers also for total and classical correlations finding, for a quite general class of bipartite states, their explicit expressions. We analyze the relationship among geometric total, quantum and classical correlations and we find that they do not satisfy anymore a closed additivity relation.

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Entanglement Irreversibility from Quantum Discord and Quantum Deficit

Cited by 115 publications

References 28 publications

The classical-quantum boundary for correlations: Discord and related measures

The classical-quantum boundary for correlations: Discord and related measures

Necessary and sufficient condition for saturating the upper bound of quantum discord

Unified view of correlations using the square-norm distance

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