论文标题
WishArt和随机密度矩阵：均方体Hilbert-Schmidt距离的分析结果
Wishart and random density matrices: Analytical results for the mean-square Hilbert-Schmidt distance
论文作者
论文摘要
希尔伯特·史克米特（Hilbert-Schmidt）距离是量子信息理论中突出的距离度量之一，它在各种问题中找到了应用，例如纠缠证人的构建，机器学习中的量子算法和量子状态层析成像。在这项工作中，我们计算了均方根密度矩阵和固定密度矩阵之间的均方根Hilbert-Schmidt距离以及两个随机密度矩阵之间的精确而紧凑的结果。在派生过程中，我们还获得了固定矩阵和固定的赫米尔族矩阵和两个Wishart矩阵之间距离的相应确切结果。我们使用Monte Carlo模拟验证我们的所有分析结果。最后，我们应用结果来研究使用耦合踢顶产生的降低密度矩阵之间的Hilbert-Schmidt距离。
Hilbert-Schmidt distance is one of the prominent distance measures in quantum information theory which finds applications in diverse problems, such as construction of entanglement witnesses, quantum algorithms in machine learning, and quantum state tomography. In this work, we calculate exact and compact results for the mean square Hilbert-Schmidt distance between a random density matrix and a fixed density matrix, and also between two random density matrices. In the course of derivation, we also obtain corresponding exact results for the distance between a Wishart matrix and a fixed Hermitian matrix, and two Wishart matrices. We verify all our analytical results using Monte Carlo simulations. Finally, we apply our results to investigate the Hilbert-Schmidt distance between reduced density matrices generated using coupled kicked tops.
