Quantum interpolating ensemble: Biorthogonal polynomials and average entropies

• URL: http://arxiv.org/abs/2103.04231v2
• Date: Wed, 24 May 2023 20:05:30 GMT
• Title: Quantum interpolating ensemble: Biorthogonal polynomials and average entropies
• Authors: Lu Wei and Nicholas Witte
• Abstract summary: The average of quantum purity and von Neumann entropy for an ensemble interpolates between the Hilbert-Schmidt and Bures-Hall ensembles. The proposed interpolating ensemble is a specialization of the $theta$-deformed Cauchy-Laguerre two-matrix model.
• Score: 3.8265321702445267
• License: http://creativecommons.org/licenses/by/4.0/
• 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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