Why entanglement of formation is not generally monogamous

Fanchini, Felipe F.; Oliveira, M. C. de; Castelano, L. K.; Cornelio, Marcio F.

doi:10.1103/physreva.87.032317

Cited by 42 publications

(28 citation statements)

References 30 publications

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“…We should also point out that for pure states of three qubits there is a conservation law between discord and EF, such that E 12 + E 13 = D 12 + D 13 [11]. So the monogamies of the two quantum correlations are tightly connected, and a violation of one would imply of the other, something already noted before by some of us [16]. These relations are obtained from the Koashi-Winter (KW) relation E 12 + J ← 13 = S 1 [4], where J ← 13 is the one-way classical correlation between 1 and 3 [17,18].…”

Section: B Monogamy For the Linear Versionmentioning

confidence: 62%

Monogamy of entanglement of formation

2014

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It is well known that a particle cannot freely share entanglement with two or more particles. This restriction is generally called monogamy. However the formal quantification of such restriction is only known for some measures of entanglement and for two-level systems. The first and broadly known monogamy relation was established by Coffman, Kundu, and Wootters for the square of the concurrence. Since then, it is usually said that the entanglement of formation is not monogamous, as it does not obey the same relation. We show here that despite that, the entanglement of formation cannot be freely shared and therefore should be said to be monogamous. Furthermore, the square of the entanglement of formation does obey the same relation of the squared concurrence, a fact recently noted for three particles and extended here for N particles. Therefore the entanglement of formation is as monogamous as the concurrence. We also numerically study how the entanglement is distributed in pure states of three qubits and the relation between the sum of the bipartite entanglement and the classical correlation.

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Section: B Monogamy For the Linear Versionmentioning

confidence: 62%

Monogamy of entanglement of formation

2014

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“…A way to deal with this might involve a hybrid approach to monogamy of correlations, when both quantum and classical correlations are present, as suggests. Finally, (Fanchini et al, 2011b) argue that the relationship between quantum and classical correlations is at the heart of why entanglement of formation is not monogamous.…”

Section: Monogamy Of Discordmentioning

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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“…It should be noted that, in the monogamy relation, the square of concurrence is monogamous other than the concurrence itself which is not monogamous. Previous studies indicated that the QD is not monogamous even in three-qubit pure states [25][26][27][28][29], which does not imply that the square of QD is not monogamous either.…”

Section: A Definitions and Monogamous Conditionmentioning

confidence: 99%

Exploring multipartite quantum correlations with the square of quantum discord

Bai

Zhang

et al. 2013

Phys. Rev. A

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We explore the quantum correlation distribution in multipartite quantum states based on the square of quantum discord (SQD). For tripartite quantum systems, we derive the necessary and sufficient condition for the SQD to satisfy the monogamy relation. Particularly, we prove that the SQD is monogamous for three-qubit pure states, based on which a genuine tripartite quantum correlation measure is introduced. In addition, we also address the quantum correlation distributions in four-qubit pure states. As an example, we investigate multipartite quantum correlations in the dynamical evolution of multipartite cavity-reservoir systems.

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Why entanglement of formation is not generally monogamous

Cited by 42 publications

References 30 publications

Monogamy of entanglement of formation

Monogamy of entanglement of formation

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

Exploring multipartite quantum correlations with the square of quantum discord

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