Related papers: Limiting spectral distribution of random self-adjoint quantum channels

Limiting spectral distribution of random self-adjoint quantum channels

URL: http://arxiv.org/abs/2311.12368v1
Date: Tue, 21 Nov 2023 06:15:29 GMT
Title: Limiting spectral distribution of random self-adjoint quantum channels
Authors: C\'ecilia Lancien, Patrick Oliveira Santos, and Pierre Youssef
Abstract summary: We show that when the Kraus rank goes to infinity with n, the limiting spectral distribution coincides with the semi-circle distribution. When the Kraus rank is fixed, the limiting spectral distribution is no longer the semi-circle distribution.
Score: 0.0
License: http://creativecommons.org/licenses/by/4.0/
Abstract: We study the limiting spectral distribution of quantum channels whose Kraus operators are sampled as $n\times n$ random Hermitian matrices satisfying certain assumptions. We show that when the Kraus rank goes to infinity with n, the limiting spectral distribution (suitably rescaled) of the corresponding quantum channel coincides with the semi-circle distribution. When the Kraus rank is fixed, the limiting spectral distribution is no longer the semi-circle distribution. It corresponds to an explicit law, which can also be described using tools from free probability.

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