Hilbert-Schmidt Separability Probabilities from Bures Ensembles and vice versa: Applications to Quantum Steering Ellipsoids and Monotone Metrics

2021/01/19 by Paul B. Slater, Slater, Paul B.
Mathematics · Physics and Astronomy · #Random Matrices and Applications #Benford’s Law and Fraud Detection #Statistical Mechanics and Entropy

paper · pdf · doi:10.48550/arxiv.2101.07716

Abstract

We reexamine a recent analysis in which, using the volume of the associated quantum steering ellipsoid (QES) as a measure, we sought to estimate the probability that a two-qubit state is separable. In the estimation process, we, in effect, sought to attach to states random with respect to Hilbert-Schmidt (HS) measure, the corresponding QES volumes. However, a study of the relations between HS and Bures ensembles and their well-supported separability probabilities of (8)/(33) and (25)/(341), respectively, now lead us to explore as a possible alternative measure, the QES volume divided by the Π_j

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