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.
CITATION STYLE
Forrester, P. J., & Kieburg, M. (2016). Relating the Bures Measure to the Cauchy Two-Matrix Model. Communications in Mathematical Physics, 342(1), 151–187. https://doi.org/10.1007/s00220-015-2435-4
Mendeley helps you to discover research relevant for your work.