高斯量子态的曲率
Curvature of Gaussian quantum states
AI总结：
本文研究高斯量子态流形的几何曲率，发现曲率随冯·诺依曼熵严格单调，可作为态不确定性度量，并为连续变量系统中的佩茨猜想提供证据。
摘要：
量子态空间可以通过相对熵的二阶导数赋予度量结构，从而产生所谓的久保-森-博戈留博夫内积。我们在由协方差矩阵参数化的忠实、零位移高斯态子流形上探讨其几何性质，推导出测地线方程、曲率张量和标量曲率的表达式。我们的分析表明，该流形的曲率关于冯·诺依曼熵严格单调，因此可被解释为态不确定性的度量。这为连续变量系统中的佩茨猜想提供了支持性证据。
英文摘要：
The space of quantum states can be endowed with a metric structure using the second order derivatives of the relative entropy, giving rise to the so-called Kubo-Mori-Bogoliubov inner product. We explore its geometric properties on the submanifold of faithful, zero-displacement Gaussian states parameterised by their covariance matrices, deriving expressions for the geodesic equations, curvature tensors and scalar curvature. Our analysis suggests that the curvature of the manifold is strictly monotonic with respect to the von Neumann entropy, and thus can be interpreted as a measure of state uncertainty. This provides supporting evidence for the Petz conjecture in continuous variable systems.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
