近日，中国科学院数学与系统科学研究院的骆顺龙及其研究小组与南京师范大学的孙源合作并取得一项新进展。经过不懈努力，他们利用消失基相关性表征两体态。相关研究成果已于2024年8月13日在国际知名学术期刊《物理评论A》上发表。

在这项工作中，研究人员关注由全局态与相对于局部基的局部态之间的相干性差异所定义的双态中的基依赖相关性，并对具有消失基依赖相关性的双态进行表征。Yadin等人[Phys. Rev. X 6, 041028 (2016)]使用相对熵相干性确定了此类态的结构，研究人员在此称之为块对角乘积态。本工作的第一个成果是证明，使用基于偏斜信息的相干性度量，块对角乘积态集合也可以通过具有消失基依赖相关性的性质进行表征。

作为这一结果的副产物，研究人员描述了使用基于偏斜信息的相干性度量在相干性资源理论中使凸性不等式达到饱和的量子系综的结构，这可能具有独立的研究意义。接下来，研究人员使用相干性的l₁范数对具有消失基依赖相关性的双态集合进行表征，并证明块对角乘积态集合是其子集。

此外，他们在一个干涉模型中为块对角乘积态提供了操作解释。最后，他们通过维尔纳态、各向同性态、贝尔对角态以及一类经典-量子态等示例，比较了使用上述三种相干性度量得到的基依赖相关性的量。

据悉，由于相干性和量子相关性都源于叠加原理，并且都可以被视为量子信息任务中的资源，因此从不同角度研究它们之间的相互作用具有重要意义。

附：英文原文

Title: Characterizing bipartite states with vanishing basis-dependent correlations

Author: Nan Li, Zijian Zhang, Shunlong Luo, Yuan Sun

Issue&Volume: 2024/08/13

Abstract: Since both coherence and quantum correlations arise from the superposition principle and can be regarded as resources in quantum information tasks, it is of significance to investigate the interplay between them from different perspectives. In this work we focus on the basis-dependent correlations in a bipartite state defined by the coherence difference between global state and local state relative to a local basis and characterize bipartite states with vanishing basis-dependent correlations. Using the relative entropy of coherence, the structure of such states has been determined by Yadin et al. [Phys. Rev. X 6, 041028 (2016)], which we call block-diagonal product states here. The first result of this work is to demonstrate that the set of block-diagonal product states can also be characterized by the property of possessing vanishing basis-dependent correlations using the coherence measure based on skew information. As a by-product of this result, we describe the structure of quantum ensembles saturating the convexity inequality in the resource theory of coherence using the coherence measure based on skew information, which may be of independent interest. Next, we characterize the set of bipartite states with vanishing basis-dependent correlations using the l₁ norm of coherence, and show that the set of block-diagonal product states is a subset of it. Furthermore, we provide an operational interpretation of block-diagonal product states in an interference model. Finally, we compare the amount of basis-dependent correlations using the three mentioned coherence measures through several examples such as Werner states, isotropic states, Bell-diagonal states, and a family of classical-quantum states.

DOI: 10.1103/PhysRevA.110.022418

Source: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.110.022418