Complete entropy contraction from conditional hyperboundedness

Li Gao; Lijun Wang

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arXiv · 2610.35863

Complete entropy contraction from conditional hyperboundedness

Li Gao·Lijun Wang

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Abstract

For finite-dimensional quantum channels compatible with a faithful conditional expectation, we show that conditional hyperboundedness and strict GNS contraction together yield a relative entropy contraction. For KMS-symmetric quantum Markov semigroups, a conditional $2\to q$ hyperboundedness at time $t_0>0$ combined with a GNS gap $λ>0$ implies a modified logarithmic Sobolev constant \[ α=\frac{λ(1-2/q)} {12(λt_0+\log M+1-2/q)},\] where $M$ is the hyperboundedness constant. As a consequence, completely bounded hyperboundedness over auxiliary systems gives complete versions of entropy contraction with the same rates.

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Li Gao, Lijun Wang. 2026-10-26. Complete entropy contraction from conditional hyperboundedness. https://arxiv.org/abs/2610.35863

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