Moments of quantum purity and biorthogonal polynomial recurrence
- URL: http://arxiv.org/abs/2107.04637v1
- Date: Fri, 9 Jul 2021 19:18:34 GMT
- Title: Moments of quantum purity and biorthogonal polynomial recurrence
- Authors: Shi-Hao Li and Lu Wei
- Abstract summary: We study the statistical behavior of entanglement over the Bures-Hall ensemble as measured by the simplest form of an entanglement entropy - the quantum purity.
The main results of this work are the exact second and third moment expressions of quantum purity valid for any subsystem dimensions.
- Score: 6.482224543491085
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: The Bures-Hall ensemble is a unique measure of density matrices that
satisfies various distinguished properties in quantum information processing.
In this work, we study the statistical behavior of entanglement over the
Bures-Hall ensemble as measured by the simplest form of an entanglement entropy
- the quantum purity. The main results of this work are the exact second and
third moment expressions of quantum purity valid for any subsystem dimensions,
where the corresponding results in the literature are limited to the scenario
of equal subsystem dimensions. In obtaining the results, we have derived
recurrence relations of the underlying integrals over the Cauchy-Laguerre
biorthogonal polynomials that may be of independent interest.
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