Communications in Mathematical Physics

, Volume 342, Issue 1, pp 151–187 | Cite as

Relating the Bures Measure to the Cauchy Two-Matrix Model

  • Peter J. Forrester
  • Mario KieburgEmail author


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.


Partition Function Random Matrice Random Matrix Density Operator Characteristic Polynomial 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsThe University of MelbourneParkvilleAustralia
  2. 2.Fakultät für PhysikUniversität Bielefeld, Postfach 100131BielefeldGermany

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