TY - JOUR
T1 - Limiting Spectral Distribution of Random Self-Adjoint Quantum Channels
AU - Lancien, Cécilia
AU - Oliveira Santos, Patrick
AU - Youssef, Pierre
N1 - Publisher Copyright:
© The Author(s), under exclusive licence to Springer Nature B.V. 2024.
PY - 2024/9
Y1 - 2024/9
N2 - We study the limiting spectral distribution of quantum channels whose Kraus operators sampled as n×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.
AB - We study the limiting spectral distribution of quantum channels whose Kraus operators sampled as n×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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U2 - 10.1007/s11040-024-09482-z
DO - 10.1007/s11040-024-09482-z
M3 - Article
AN - SCOPUS:85200508238
SN - 1385-0172
VL - 27
JO - Mathematical Physics Analysis and Geometry
JF - Mathematical Physics Analysis and Geometry
IS - 3
M1 - 15
ER -