Complete entropy contraction from conditional hyperboundedness

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.

Source: arXiv:2610.35863v1 - http://arxiv.org/abs/2610.35863v1 PDF: https://arxiv.org/pdf/2610.35863v1 Original Link: http://arxiv.org/abs/2610.35863v1