Purity distribution for generalized random Bures mixed states

Abstract

We compute the distribution of the purity for random density matrices (i.e.random mixed states) in a large quantum system, distributed according to the Bures measure. The full distribution of the purity is computed using a mapping to random matrix theory and then a Coulomb gas method. We find three regimes that correspond to two phase transitions in the associated Coulomb gas. The first transition is characterized by an explosion of the third derivative on the left of the transition point. The second transition is of first order, it is characterized by the detachement of a single charge of the Coulomb gas. A key remark in this paper is that the random Bures states are closely related to the O(n) model for n=1. This actually led us to study "generalized Bures states" by keeping $n$ general instead of specializing to n=1.

References in corpus (15)

• Large Deviations of Extreme Eigenvalues of Random Matrices
• Extreme Value Statistics of Eigenvalues of Gaussian Random Matrices
• Large Deviations of the Maximum Eigenvalue for Wishart and Gaussian Random Matrices
• Statistical distribution of quantum entanglement for a random bipartite state
• Phase Transitions in the Distribution of Bipartite Entanglement of a Random Pure State
• Large Deviations of the Maximum Eigenvalue in Wishart Random Matrices
• The Index Distribution of Gaussian Random Matrices
• Distributions of Conductance and Shot Noise and Associated Phase Transitions
• How many eigenvalues of a Gaussian random matrix are positive?
• Probability distributions of Linear Statistics in Chaotic Cavities and associated phase transitions
• The volume of separable states is super-doubly-exponentially small
• Phase transitions and metastability in the distribution of the bipartite entanglement of a large quantum system
• Exact Minimum Eigenvalue Distribution of an Entangled Random Pure State
• Distribution of G-concurrence of random pure states
• Enumeration of maps with self avoiding loops and the O(n) model on random lattices of all topologies

Cited by in corpus (12)

• Relating the Bures measure to the Cauchy two-matrix model
• Exact variance of von Neumann entanglement entropy over the Bures-Hall measure
• Non-crossing Brownian paths and Dyson Brownian motion under a moving boundary
• Second-order statistics of fermionic Gaussian states
• Average capacity of quantum entanglement
• Fluctuations in the two-dimensional one-component plasma and associated fourth-order phase transition
• Quantum interpolating ensemble: Biorthogonal polynomials and average entropies
• Numerical and Exact Analyses of Bures and Hilbert-Schmidt Separability and PPT-Probabilities
• Extensions of Generalized Two-Qubit Separability Probability Analyses to Higher Dimensions, Additional Measures and New Methodologies
• Entanglement capacity of fermionic Gaussian states
• Entanglement transitions induced by large deviations
• Moments of quantum purity and biorthogonal polynomial recurrence