Phase Transitions in the Distribution of Bipartite Entanglement of a Random Pure State

Abstract

Using a Coulomb gas method, we compute analytically the probability distribution of the Renyi entropies (a standard measure of entanglement) for a random pure state of a large bipartite quantum system. We show that, for any order q>1 of the Renyi entropy, there are two critical values at which the entropy's probability distribution changes shape. These critical points correspond to two different transitions in the corresponding charge density of the Coulomb gas: the disappearance of an integrable singularity at the origin and the detachement of a single-charge drop from the continuum sea of all the other charges. These transitions respectively control the left and right tails of the entropy's probability distribution, as verified also by Monte Carlo numerical simulations of the Coulomb gas equilibrium dynamics.

4 pages revtex, 2 figures included

References in corpus (10)

• Large Deviations of Extreme Eigenvalues of Random Matrices
• Extreme Value Statistics of Eigenvalues of Gaussian Random Matrices
• Maximally multipartite entangled states
• Large Deviations of the Maximum Eigenvalue for Wishart and Gaussian Random Matrices
• 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
• Probability distributions of Linear Statistics in Chaotic Cavities and associated phase transitions
• Entanglement of random vectors
• Exact Minimum Eigenvalue Distribution of an Entangled Random Pure State

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