Quantum interpolating ensemble: Biorthogonal polynomials and average entropies
arXiv:2103.04231 · doi:10.1142/S2010326322500551
Abstract
The density matrix formalism is a fundamental tool in studying various problems in quantum information processing. In the space of density matrices, the most well-known measures are the Hilbert-Schmidt and Bures-Hall ensembles. In this work, the averages of quantum purity and von Neumann entropy for an ensemble that interpolates between these two major ensembles are explicitly calculated for finite-dimensional systems. The proposed interpolating ensemble is a specialization of the -deformed Cauchy-Laguerre two-matrix model and new results for this latter ensemble are given in full generality, including the recurrence relations satisfied by their associated bi-orthogonal polynomials when assumes positive integer values.
arXiv comment29 pages, 4 figures
References in corpus (33)
- Average Entropy of a Subsystem
- Induced measures in the space of mixed quantum states
- Aspects of generic entanglement
- Generating random density matrices
- Bures volume of the set of mixed quantum states
- Statistical properties of random density matrices
- Random quantum correlations and density operator distributions
- Average fidelity between random quantum states
- Statistical distribution of quantum entanglement for a random bipartite state
- The Cauchy two-matrix model
- Random Bures mixed states and the distribution of their purity
- The volume of separable states is super-doubly-exponentially small
- Random pure states: quantifying bipartite entanglement beyond the linear statistics
- Bounds on entanglement in qudit subsystems
- Distribution of bipartite entanglement for random pure states
- Cauchy-Laguerre two-matrix model and the Meijer-G random point field
- Entanglement thresholds for random induced states
- A Proof of Vivo-Pato-Oshanin's Conjecture on the Fluctuation of von Neumann Entropy
- Relating the Bures measure to the Cauchy two-matrix model
- Generalized Entanglement Entropies of Quantum Designs
- Average Entropy of a Subsystem from its Average Tsallis Entropy
- Bures-Hall Ensemble: Spectral Densities and Average Entropies
- Smallest eigenvalue distribution of the fixed trace Laguerre beta-ensemble
- The Cauchy two-matrix model, C-Toda lattice and CKP hierarchy
- Exact variance of von Neumann entanglement entropy over the Bures-Hall measure
- Skewness of von Neumann entanglement entropy
- On the exact variance of Tsallis entropy in a random pure state
- Proof of Sarkar-Kumar's Conjectures on Average Entanglement Entropies over the Bures-Hall Ensemble
- Purity distribution for generalized random Bures mixed states
- On the Bures Volume of Separable Quantum States
- Kurtosis of von Neumann entanglement entropy
- Numerical and Exact Analyses of Bures and Hilbert-Schmidt Separability and PPT-Probabilities
- Moments of quantum purity and biorthogonal polynomial recurrence