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

Xi, Zhengjun; Lu, Xiao-Ming; Wang, Xiaoguang; Li, Yongming

doi:10.1103/physreva.85.032109

Cited by 32 publications

(37 citation statements)

References 49 publications

(85 reference statements)

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“…For this question, some class of states have been given in Refs. [11,16], which conform Luo et al's conjecture [10].…”

Section: Introductionsupporting

confidence: 87%

“…Particularly, it has been proved that it is impossible to obtain a closed expression for QD, even for general states of two qubits [9]. This fact makes it desirable to obtain some computable bounds for QD, and several attempts have been devoted * gaofei bupt@hotmail.com to this issue in the past few years [10][11][12].…”

Section: Introductionmentioning

confidence: 99%

“…Under these conditions, it has been proved [14,[16][17] that QD is upper bounded by the von Neumann entropy of the measured subsystem. Recently, Xi et al [11] revisited the upper bound of QD given by the von Neumann entropy of the measured subsystem using a tradeoff between the amount of classical correlation and QD in a tripartite pure state.…”

Section: Introductionmentioning

confidence: 99%

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General bounds for quantum discord and discord distance

Liu

Tian

Wen

et al. 2015

Quantum Inf Process

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For any bipartite state, how strongly can one subsystem be quantum correlated with another? Using the Koashi-Winter relation, we study the upper bound of purified quantum discord, which is given by the sum of the von Neumann entropy of the unmeasured subsystem and the entanglement of formation shared between the unmeasured subsystem with the environment. In particular, we find that the Luo et al.'s conjecture on the quantum correlations and the Lindblad conjecture are all ture, when the entanglement of formation vanishes. Let the difference between the left discord and the right discord be captured by the discord distance. If the Lindblad conjecture is true, we show that the joint entropy is a tight upper bound for the discord distance. Further, we obtain a necessary and sufficient condition for saturating upper bounds of purified quantum discord and discord distance separately with the equality conditions for the Araki-Lieb inequality and the Lindblad conjecture. Furthermore, we show that the subadditive relation holds for any bipartite quantum discord.

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“…For this question, some class of states have been given in Refs. [11,16], which conform Luo et al's conjecture [10].…”

Section: Introductionsupporting

confidence: 87%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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General bounds for quantum discord and discord distance

Liu

Tian

Wen

et al. 2015

Quantum Inf Process

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“…General bounds for discord Xi et al, 2011) prove a very general bound relating discord to the von Neumann entropy of the measured subsystem: D(B|A) ≤ S(A). Determining which states saturate this bound is more demanding, and was done in (Xi et al, 2012). The inequality is saturated if and only if there is a decomposition of the Hilbert space for B,…”

Section: Conservation Lawmentioning

confidence: 99%

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

et al. 2012

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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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“…As shown in Ref. [40], this state can be factorized as in Eq. (17) with |ψ AB L = (|00 + |11 )/ √ 2 and ρ B R = I B R /2, and as a result gives the negative conditional entropy S(A|B) = −S(ρ A ) = −1.…”

Section: Negative Conditional Entropymentioning

confidence: 99%

Competition between quantum correlations in the quantum-memory-assisted entropic uncertainty relation

Fan

2013

Phys. Rev. A

117

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With the aid of a quantum memory, the uncertainty about the measurement outcomes of two incompatible observables of a quantum system can be reduced. We investigate this measurement uncertainty bound by considering an additional quantum system connected with both the quantum memory and the measured quantum system. We find that the reduction of the uncertainty bound induced by a quantum memory, on the other hand, implies its increasing for a third participant. We also show that the properties of the uncertainty bound can be viewed from perspectives of both quantum and classical correlations, in particular, the behavior of the uncertainty bound is a result of competitions of various correlations between different parties.

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

Cited by 32 publications

References 49 publications

General bounds for quantum discord and discord distance

General bounds for quantum discord and discord distance

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

Competition between quantum correlations in the quantum-memory-assisted entropic uncertainty relation

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