近日，日本电气通信大学的Daigo Kudo&Hiroyasu Tajima研究小组取得一项新进展。经过不懈努力，他们发现在具备通用连通李群对称的不对称资源理论中，Fisher信息矩阵可用作一种资源度量方法。相关成果已于2023年6月20日在国际知名学术期刊《物理评论A》上发表。
据悉，近年来量子信息理论中对研究动力学对称性的一般理论框架有了显著的发展，被称为非对称性资源理论，并预计将在大量领域应用，包括精确时间测量和黑洞物理。尽管非对称性资源理论的重要性已被认可，但其基础仍有待完善。其中一个重要问题是如何量化资源的数量。当对称性规定为U(1)或R，即具有单个守恒量时，已经确认了量子费舍信息作为一种资源度量，具有适当的性质并与守恒量的量子涨落有明确的物理意义。然而，在存在多个守恒量的一般对称性情况下，目前尚不清楚是否存在具有适当性质的资源度量。本研究的目的在于填补这一研究空白。
具体而言，该研究团队取得了重要进展，他们证明了当一个连通的线性李群描述对称性时，量子费舍信息矩阵可以作为一种资源度量。此外，他们还研究了该矩阵的物理意义，并探讨了当对称性由U(1)或R描述时，量子费舍信息矩阵可以继承哪些性质。这一发现对于非对称性资源理论的进一步发展具有重要意义。
附：英文原文
Title: Fisher information matrix as a resource measure in the resource theory of asymmetry with general connected-Lie-group symmetry
Author: Daigo Kudo, Hiroyasu Tajima
Issue&Volume: 2023/06/20
Abstract: In recent years, in quantum information theory, there has been a remarkable development in the general theoretical framework for studying symmetry in dynamics. This development, called resource theory of asymmetry, is expected to have a wide range of applications, from accurate time measurements to black-hole physics. Despite its importance, the foundation of resource theory of asymmetry still has room for expansion. An important problem is in quantifying the amount of resource. When the symmetry prescribed U(1) or R, i.e., with a single conserved quantity, the quantum Fisher information is known as a resource measure that has suitable properties and a clear physical meaning related to quantum fluctuation of the conserved quantity. However, it is not clear what is the resource measure with such suitable properties when a general symmetry prevails for which there are multiple conserved quantities. The purpose of this paper is to fill this gap. Specifically, we show that the quantum Fisher information matrix is a resource measure whenever a connected linear Lie group describes the symmetry. We also consider the physical meaning of this matrix and see which properties that the quantum Fisher information has when the symmetry is described by U(1) or R can be inherited by the quantum Fisher information matrix.
DOI: 10.1103/PhysRevA.107.062418
Source: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.107.062418
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