Limiting spectral distribution of random self-adjoint quantum channels

Cécilia Lancien; Patrick Oliveira Santos; Pierre Youssef

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arXiv · 2311.12368

Limiting spectral distribution of random self-adjoint quantum channels

Cécilia Lancien·Patrick Oliveira Santos·Pierre Youssef

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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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Cécilia Lancien, Patrick Oliveira Santos, Pierre Youssef. 2023-11-21. Limiting spectral distribution of random self-adjoint quantum channels. https://arxiv.org/abs/2311.12368

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