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Physical Review A

Tsallis entropy and general polygamy of multiparty quantum entanglement in arbitrary dimensions

Jeong San Kim

Published Dec 28, 2016• 44 citations
Publisher

Abstract

We establish a unified view of the polygamy of multiparty quantum entanglement in arbitrary dimensions. Using quantum Tsallis-$q$ 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 $q$. We further provide one-parameter generalizations of various quantum correlations based on Tsallis-$q$ entropy. By investigating the properties of the generalized quantum correlations, we provide a sufficient condition on which the Tsallis-$q$ polygamy inequalities hold in multiparty quantum systems of arbitrary dimensions.

DOI
10.1103/physreva.94.062338

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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.
We characterize the polygamy nature of quantum entanglement in multiparty systems in terms of qqq-expectation value for the full range of $q\ensuremath{\ge}1$. 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 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 $q\ensuremath{\ge}1$.
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 provide a generalization for the polygamy constraint of multiparty entanglement in arbitrary-dimensional quantum systems. By using the $\ensuremath{\beta}\mathrm{th}$ power of entanglement of assistance for $0\ensuremath{\le}\ensuremath{\beta}\ensuremath{\le}1$ and the Hamming weight of the binary vector related with the distribution of subsystems, we establish a class of weighted polygamy inequalities of multiparty entanglement in arbitrary-dimensional quantum systems. We further show that our class of weighted polygamy inequalities can even be improved to be tighter inequalities with some conditions on the assisted entanglement of bipartite subsystems.