论文标题
Fisher Information Matrix作为与一般连接的Lie组对称的不对称资源理论的资源度量
Fisher information matrix as a resource measure in resource theory of asymmetry with general connected Lie group symmetry
论文作者
论文摘要
近年来，在量子信息理论中，在研究动力学中的对称性的一般理论框架中有一个显着的发展。这种称为不对称资源理论的发展有望具有广泛的应用，从准确的时间测量到黑洞物理。尽管它很重要，但不对称资源理论的基础仍然有扩展的空间。一个重要的问题是量化资源量。当对称性规定的u（1），即带有单个保守数量时，量子渔民信息被称为一种资源度量，具有合适的特性和与保守数量的量子波动有关的清晰的物理含义。但是，尚不清楚当一般对称性占有多个保守数量时，具有这种合适属性的资源度量是什么。本文的目的是填补这一空白。具体来说，我们表明，每当连接的线性谎言组描述对称性时，量子Fisher信息矩阵是一种资源度量。我们还考虑了此矩阵的物理含义，并查看量子Fisher信息在$ u（1）$描述时具有哪些属性，可以继承量子Fisher Information矩阵。
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), 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 $U(1)$ can be inherited by the quantum Fisher information matrix.
