标题： 多参数量子信息中的半经典几何张量 显示英文标题

标题： Semi-classical geometric tensor in multiparameter quantum information

摘要： 量子几何张量（QGT）捕捉了量子态随参数变化的情况，在现代量子物理中是一个核心概念。 其实部，即量子费舍尔信息矩阵（QFIM），有一个与测量相关的对应物，将统计学与可区分性联系起来。 然而，由于通过测量概率无法根本上获取其虚部，因此QGT的类似扩展受到阻碍。 在这里，我们引入了一个包含测量算子的QGT的对应物，称为\textit{半经典}几何张量（SCGT）。 我们证明了SCGT为QGT提供了一个下界，对于纯态来说这个下界是紧致的。 此外，我们利用SCGT推导出精确的多参数信息界限，并讨论了贝里相位的扩展。 显示英文摘要

摘要： The quantum geometric tensor (QGT) captures the variations of quantum states with parameters, serving as a central concept in modern quantum physics. Its real part, the quantum Fisher information matrix (QFIM), has a measurement-dependent counterpart that links statistics to distinguishability. However, an analogous extension for the QGT is hindered by the fundamental inaccessibility of its imaginary part through measurement probabilities. Here we introduce a counterpart to the QGT that includes measurement operators, termed the \textit{semi-classical} geometric tensor (SCGT). We show that the SCGT provides a lower bound to the QGT that is tight for pure states. Moreover, we use the SCGT to derive sharp multiparameter information bounds and discuss extensions of the Berry phase.