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arXiv · 2103.04231

Quantum interpolating ensemble: Biorthogonal polynomials and average entropies

Lu Wei·Nicholas Witte
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Abstract

The density matrix formalism is a fundamental tool in studying various problems in quantum information processing. In the space of density matrices, the most well-known measures are the Hilbert-Schmidt and Bures-Hall ensembles. In this work, the averages of quantum purity and von Neumann entropy for an ensemble that interpolates between these two major ensembles are explicitly calculated for finite-dimensional systems. The proposed interpolating ensemble is a specialization of the $\theta$-deformed Cauchy-Laguerre two-matrix model and new results for this latter ensemble are given in full generality, including the recurrence relations satisfied by their associated bi-orthogonal polynomials when $\theta$ assumes positive integer values.

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BibTeXRIS

Lu Wei, Nicholas Witte. 2021-03-07. Quantum interpolating ensemble: Biorthogonal polynomials and average entropies. https://doi.org/10.1142/s2010326322500551

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