arXiv subjects

Lizhong Huang

Publications and source records attributed to Lizhong Huang.

3 recordsLinked to original sources

arXiv2022

Complete monogamy of the multipartite quantum mutual information

Quantum mutual information (QMI) not only displays the mutual information in the system but also demonstrates some quantum correlation beyond entanglement. We explore here the two alternatives of multipartite quantum mutual information (MQMI) based on the von Neumann entropy according to the framework of the complete measure of multi-particle quantum system. We show that these two MQMI are complete, monogamous on pure states, and one of them is not only completely monogamous but also tightly complete monogamous while another one is not. Moreover, we present another two MQMI by replacing the von Neumann entropy with the Tasllis $q$-entropy from the former two ones. It is proved that one of them displays some degree of ``completeness'' as a measure of multi-particle quantum system, but the other one is not even non-negative and thus it can not be a alternative of MQMI. We also discuss the triangle relation for these three alternatives of MQMI. It is shown that the triangle inequalities hold for the former two MQMI as that of entanglement measure but the later one fails. By comparison, we found that the von Neumann entropy is better than other versions of entropy as desired when we characterize the quantum correlation in multi-particle system.

quant-ph↗

arXiv2022

Genuine multipartite entanglement measure

Quantifying genuine entanglement is a crucial task in quantum information theory.In this work, we give an approach of constituting genuine $m$-partite entanglement measures from any bipartite entanglement and any $k$-partite entanglement measure, $3\leq k<m$. In addition, as a complement to the three-qubit concurrence triangle proposed in [Phys. Rev. Lett., 127, 040403], we show that the triangle relation is also valid for any continuous entanglement measure and system with any dimension. We also discuss the tetrahedron structure for the four-partite system via the triangle relation associated with tripartite and bipartite entanglement respectively. For multipartite system that contains more than four parties, there is no symmetric geometric structure as that of tri- and four-partite cases.

quant-ph↗

arXiv2021

Monogamy of quantum discord

The original quantum discord (QD) is shown to be not monogamous except for the three-qubit states. Recently, a complete monogamy relation for multiparty quantum system was established for entanglement in [Phys. Rev. A. {101}, 032301~(2020)], and in addition, a new multipartite generalization of QD was proposed in [Phys. Rev. Lett. {124}, 110401~(2020)]. In this work, we firstly define the complete monogamy for this multipartite quantum discord (MQD) and the global quantum discord (GQD). MQD, with the same spirit as the complete monogamy of entanglement, is said to be completely monogamous (i) if it does not increase under coarsening of subsystems and (ii) if some given combination of subsystems reach the total amount of the correlation, then all other combination of subsystems that do not include all the given subsystems do not contain such a correlation any more. Here, coarsening of subsystems means discarding or combining some subsystems up to the given partition. Simultaneously, the complete monogamy of GQD is also defined with slight modification on the coarsening relation.Consequently, we explore all the coarsening relations of MQD and show that it is completely monogamous with a modicum assumption. In addition, with the same spirit, we investigate all the coarsening relations for GQD and show that GQD is not completely monogamous.That is, in the sense of the complete monogamy relation, MQD as a generalization of the original QD captures the nature of such a quantum correlation, and thus it is nicer than GQD as a generalization.

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