论文标题
随机密度矩阵：平均忠诚度和平方Bures距离方差的分析结果
Random density matrices: Analytical results for mean fidelity and variance of squared Bures distance
论文作者
论文摘要
量子信息理论中相关问题的关键问题之一与量子状态的区分性有关。在这种情况下，Bures距离是各种距离度量中最重要的选择之一。它也与忠诚度有关，这在量子信息理论中是另一个巨大的重要性。在这项工作中，我们得出了固定密度矩阵和随机密度矩阵之间的平方轴的平均忠诚度和方差的确切结果，也得出了两个独立的随机密度矩阵之间的距离。这些结果补充了最近获得的平均根部保真度和平方距离距离均值的结果[Phys。修订版A 104，022438（2021）]。均值和方差的可用性也使我们能够为平方释放距离的概率密度提供基于伽马分布的近似值。使用蒙特卡洛模拟证实了分析结果。此外，我们将我们的分析结果与使用耦合踢顶产生的降低密度矩阵与随机磁场中相关的自旋链系统产生的平方Bures距离的平均值和方差进行了比较。在这两种情况下，我们都会发现很好的共识。
One of the key issues in quantum information theory related problems concerns with that of distinguishability of quantum states. In this context, Bures distance serves as one of the foremost choices among various distance measures. It also relates to fidelity, which is another quantity of immense importance in quantum information theory. In this work, we derive exact results for the average fidelity and variance of the squared Bures distance between a fixed density matrix and a random density matrix, and also between two independent random density matrices. These results supplement the recently obtained results for the mean root fidelity and mean of squared Bures distance [Phys. Rev. A 104, 022438 (2021)]. The availability of both mean and variance also enables us to provide a gamma-distribution-based approximation for the probability density of the squared Bures distance. The analytical results are corroborated using Monte Carlo simulations. Furthermore, we compare our analytical results with the mean and variance of the squared Bures distance between reduced density matrices generated using coupled kicked tops, and a correlated spin chain system in a random magnetic field. In both cases, we find good agreement.
