多体复合量子系统k-积态的一类基于迹距离的关联测度

A Class of Correlation Measures Based on Trace Distance for K-Product States In Multipartite Quantum Systems

在(Quantum Information Processing,2020,19:189),作者提出了多体量子态的六个非局域关联测度.基于这些关联测度的定义,首先获得了多体复合系统k-积态的一个等价条件;其次提出了多体量子态相对于k-体分划的基于迹距离的关联测度(简记为k-PSCM),该测度可量化多体量子系统非k-积态的量子关联度;接下来,证明了其满足关联测度的一些必要物理性质,包括非负性,局部酉操作下的不变性,在局部操作和经典通信下的单调性以及凸性.

In(Quantum Information Processing,2020,19:189),the author presented six new measures of nonlocal correlation for multipartite quantum states.In this paper,motivated by these correlation measures,we firstly obtained a new equivalent condition for k-product states;Secondly,a correlation measure based on trace distance with respect to k-partition for multipartite quantum states is presented,it is simply denoted by k-product states correlation measure(k-PSCM),which can quantify the strength of quantum correlation for non-k-product states;Next,we show that k-PSCM satisfies some basic properties as a well-defined correlation measure,including nonnegativity,invariance under local unitary operations,monotonicity under local operation and classical communications and convexity.