Relating the Bures Measure to the Cauchy Two-Matrix Model

Forrester PJ, Kieburg M (2016)
COMMUNICATIONS IN MATHEMATICAL PHYSICS 342(1): 151-187.

Journal Article | Published | English

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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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Forrester PJ, Kieburg M. Relating the Bures Measure to the Cauchy Two-Matrix Model. COMMUNICATIONS IN MATHEMATICAL PHYSICS. 2016;342(1):151-187.
Forrester, P. J., & Kieburg, M. (2016). Relating the Bures Measure to the Cauchy Two-Matrix Model. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 342(1), 151-187.
Forrester, P. J., and Kieburg, M. (2016). Relating the Bures Measure to the Cauchy Two-Matrix Model. COMMUNICATIONS IN MATHEMATICAL PHYSICS 342, 151-187.
Forrester, P.J., & Kieburg, M., 2016. Relating the Bures Measure to the Cauchy Two-Matrix Model. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 342(1), p 151-187.
P.J. Forrester and M. Kieburg, “Relating the Bures Measure to the Cauchy Two-Matrix Model”, COMMUNICATIONS IN MATHEMATICAL PHYSICS, vol. 342, 2016, pp. 151-187.
Forrester, P.J., Kieburg, M.: Relating the Bures Measure to the Cauchy Two-Matrix Model. COMMUNICATIONS IN MATHEMATICAL PHYSICS. 342, 151-187 (2016).
Forrester, Peter J., and Kieburg, Mario. “Relating the Bures Measure to the Cauchy Two-Matrix Model”. COMMUNICATIONS IN MATHEMATICAL PHYSICS 342.1 (2016): 151-187.
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