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arXiv:1909.10346 · Physical Review A

Polygamy of multiparty q -expected quantum entanglement

Jeong San Kim

Published Dec 26, 2019• 4 citations
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Abstract

We characterize the polygamy nature of quantum entanglement in multiparty systems in terms of $q$-expectation value for the full range of $q\ensuremath{\ge}1$. By investigating some properties of generalized quantum correlations in terms of $q$-expectation value and Tsallis $q$-entropy, we establish a class of polygamy inequalities of multiparty quantum entanglement in arbitrary dimensions based on $q$-expected entanglement measure. As Tsallis $q$-entropy is reduced to von Neumann entropy, and $q$-expectation value becomes the ordinary expectation value when $q$ tends to 1, our results encapsulate previous results of polygamy inequalities based on von Neumann entropy as special cases.

DOI
10.1103/physreva.100.062332

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We characterize the polygamy nature of quantum entanglement in multiparty systems in terms of qqq-expectation value for the full range of q\ensuremath≥1q\ensuremath{\ge}1q\ensuremath≥1. By investigating some properties of generalized quantum correlations in terms of qqq-expectation value and Tsallis qqq-entropy, we establish a class of polygamy inequalities of multiparty quantum entanglement in arbitrary dimensions based on qqq-expected entanglement measure. As Tsallis qqq-entropy is reduced to von Neumann entropy, and qqq-expectation value becomes the ordinary expectation value when qqq tends to 1, our results encapsulate previous results of polygamy inequalities based on von Neumann entropy as special cases.
We establish a unified view of the polygamy of multiparty quantum entanglement in arbitrary dimensions. Using quantum Tsallis-qqq entropy, we provide a one-parameter class of polygamy inequalities of multiparty quantum entanglement. This class of polygamy inequalities reduces to the known polygamy inequalities based on tangle and entanglement of assistance for a selective choice of the parameter qqq. We further provide one-parameter generalizations of various quantum correlations based on Tsallis-qqq entropy. By investigating the properties of the generalized quantum correlations, we provide a sufficient condition on which the Tsallis-qqq polygamy inequalities hold in multiparty quantum systems of arbitrary dimensions.
We establish a unified view to the polygamy of multi-party quantum entanglement in arbitrary dimensions. Using quantum Tsallis-qqq entropy, we provide a one-parameter class of polygamy inequalities of multi-party quantum entanglement. This class of polygamy inequalities reduces to the known polygamy inequalities based on tangle and entanglement of assistance for a selective choice of the parameter qqq. We further provide one-parameter generalizations of various quantum correlations based on Tsallis-qqq entropy. By investigating the properties of the generalized quantum correlations, we provide a sufficient condition, on which the Tsallis-qqq polygamy inequalities hold in multi-party quantum systems of arbitrary dimensions.
Strong polygamy of multi-party qqq-expected quantum correlations
We show that the polygamous nature of multi-party quantum correlations can be characterized in a {\em stronger} form based on Tsallis qqq-entropy and qqq-expectation value. By considering the amount of entanglement that can be distributed in multi-party systems, we establish a class of strong polygamy inequalities of multi-party entanglement in terms of Tsallis qqq-entropy and qqq-expectation for q≥1q \geq 1q≥1. Our new class of inequalities is in fact tighter than the usual polygamy inequalities of multi-party entanglement, and the tightness is explicitly illustrated by an example. Moreover, our new class of inequalities is concerned with the qqq-expected entanglement distributed between a single party and any possible subsets of the rest parties whereas the usual polygamy inequality only considers the entanglement between a single party and another. We further establish the equivalence between strong polygamy inequalities of quantum entanglement and quantum discord distributed in multi-party quantum systems.
Abstract Based on q -expected entanglement measure for q ⩾ 1 , we generalize the polygamy inequality for multiparty entanglement in arbitrary-dimensional quantum systems. By using the β th-power of the q -expected entanglement of assistance for 0 ⩽ β ⩽ 1 and the Hamming weight of the binary vector related with the distribution of subsystems, a class of weighted polygamy inequalities in arbitrary-dimensional quantum systems is established. We further demonstrate that our class of weighted polygamy inequalities can be improved even into tighter inequalities, under some conditions, with auxiliary entanglement in bipartite subsystems. Our results may provide new ideas for studying the polygamy constraints of multiparty entanglement and better characterizing the entanglement distribution.
We show that the mutually exclusive nature of classical and quantum correlations distributed in multiparty quantum systems can be characterized in terms of qqq-expectation value. Using Tsallis qqq entropy and qqq-expectation value, we first provide generalized definitions of classical and quantum correlations, and establish their trade-off relations in three-party quantum systems of arbitrary dimension with respect to qqq-expectation value for $q\ensuremath{\ge}1$. We also provide equivalence conditions for monogamy and polygamy inequalities of quantum entanglement and quantum discord distributed in three-party quantum systems of arbitrary dimension with respect to qqq-expectation value for $q\ensuremath{\ge}1$.