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arXiv · 1410.6883

Relating the Bures measure to the Cauchy two-matrix model

Peter J. Forrester·Mario Kieburg
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Abstract

The Bures metric is a natural choice in measuring the distance of density operators representing states in quantum mechanics. In the past few years a random matrix ensemble and the corresponding joint probability density function of its eigenvalues was identified. Moreover a relation with the Cauchy two-matrix model was discovered but never thoroughly investigated, leaving open in particular the following question: How are the kernels of the Pfaffian point process of the Bures random matrix ensemble related to the ones of the determinantal point process of the Cauchy two-matrix model and moreover, how can it be possible that a Pfaffian point process derives from a determinantal point process? We give a very explicit answer to this question. The aim of our work has a quite practical origin since the calculation of the level statistics of the Bures ensemble is highly mathematically involved while we know the statistics of the Cauchy two-matrix ensemble. Therefore we solve the whole level statistics of a density operator drawn from the Bures prior.

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Peter J. Forrester, Mario Kieburg. 2015-04-16. Relating the Bures measure to the Cauchy two-matrix model. https://doi.org/10.1007/s00220-015-2435-4

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