Random density matrices: Analytical results for mean fidelity and variance of squared Bures distance
arXiv:2211.05587 · doi:10.1103/PhysRevE.107.034206
Abstract
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.
17 pages, 5 figures, 6 tables
References in corpus (15)
- Aspects of generic entanglement
- Statistical distribution of quantum entanglement for a random bipartite state
- Entanglement production in coupled chaotic systems : Case of the Kicked Tops
- Quantum state discrimination: a geometric approach
- On the distinguishability of random quantum states
- Exact Minimum Eigenvalue Distribution of an Entangled Random Pure State
- On the Eigenvalue Density of Real and Complex Wishart Correlation Matrices
- Bures-Hall Ensemble: Spectral Densities and Average Entropies
- Skewness of von Neumann entanglement entropy
- Wishart and random density matrices: Analytical results for the mean-square Hilbert-Schmidt distance
- Distance between Bound Entangled States from Unextendible Product Bases and Separable States
- Spectral Crossovers and Universality in Quantum Spin-chains Coupled to Random Fields
- Random density matrices: Analytical results for mean root fidelity and mean square Bures distance
- Spectral statistics for the difference of two Wishart matrices
- Estimating the precision for quantum process tomography