Non-monogamy of quantum discord and upper bounds for quantum correlation

Ren, Xi-Jun; Fan, Heng

doi:10.26421/qic13.5-6-7

Cited by 12 publications

(15 citation statements)

References 33 publications

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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: 90%

“…is not satisfied even for the three-qubit W state [25]. Giorgi [26] and Fanchini et al [27,28] related the monogamy condition of QD to the entanglement of formation, while Ren and Fan showed that QD is not monogamous under the same measurement party [29]. Recently, Streltsov et al further showed that the monogamy relation does not hold in general for quantum correlation measures which are nonzero for separable states [30].…”

Section: Introductionmentioning

confidence: 99%

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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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Section: A Definitions and Monogamous Conditionmentioning

confidence: 90%

Section: Introductionmentioning

confidence: 99%

Exploring multipartite quantum correlations with the square of quantum discord

Bai

Zhang

et al. 2013

Phys. Rev. A

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“…However, Eq. ( 8) is not valid for many entanglement measures [22,[29][30][31][32][33][34]38] and quantum discord [19] but some power function of Q admits the monogamy relation [i.e., Q α (A|BC) ≥ Q α (AB) + Q α (AC) for some α > 0]. In Ref.…”

Section: B Monogamy Relationmentioning

confidence: 99%

“…Therefore Proposition 6. The multipartite discord D A1;A2;••• ;An is completely monogamous provided that the condition (19) is valid.…”

Section: B the Four-partite Casementioning

confidence: 99%

“…In this context, there are two ways to describe these distribution: one is the monogamy or polygamy relation by the bipartite correlation measure [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41] and the other one is the relation based on the multipartite correlation measure [43][44][45]. For the bipartite measure of quantum discord, although the square of quantum discord obeys the monogamy relation for three qubit states [19], other systems always display polygamous behaviour [17][18][19][20][21]. In Ref.…”

Section: Introductionmentioning

confidence: 99%

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Monogamy of quantum discord

Guo,

Huang,

Zhang

2021

Preprint

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We explore all the trade-off relations of multipartite quantum discord proposed very recently in [Phys. Rev. Lett. 124, 110401 (2020)] and show that the multipartite quantum discord is completely monogamous provided that it does not increase under discard of subsystems. Here, a quantity of multipartite quantity, with the same spirit as established in [Phys. Rev. A. 101, 032301 (2020)], is said to be completely monogamous (i) if it does not increase under loss of subsystems and (ii) if some given combination of subsystems reach the total amout of correlation, then all other combination of subsystems that excluding the given subsystems do not contain such a correlation any more. In addition, we explore all the trade-off relations for the global quantum discord proposed in [Phys. Rev. A 84, 042109 (2011)] and show that the global quantum discord is not completely monogamous.

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Monogamy of Quantum Correlations - A Review

Dhar

Pal

Rakshit

et al. 2017

Quantum Science and Technology

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Monogamy is an intrinsic feature of quantum correlations that gives rise to several interesting quantum characteristics which are not amenable to classical explanations. The monogamy property imposes physical restrictions on unconditional sharability of quantum correlations between the different parts of a multipartite quantum system, and thus has a direct bearing on the cooperative properties of states of multiparty systems, including large many-body systems. On the contrary, a certain party can be maximally classical correlated with an arbitrary number of parties in a multiparty system. In recent years, the monogamy property of quantum correlations has been applied to understand several key aspects of quantum physics, including distribution of quantum resources, security in quantum communication, critical phenomena, and quantum biology. In this chapter, we look at some of the salient developments and applications in quantum physics that have been closely associated with the monogamy of quantum discord, and "discord-like" quantum correlation measures.

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Non-monogamy of quantum discord and upper bounds for quantum correlation

Cited by 12 publications

References 33 publications

Exploring multipartite quantum correlations with the square of quantum discord

Exploring multipartite quantum correlations with the square of quantum discord

Monogamy of quantum discord

Monogamy of Quantum Correlations - A Review

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