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Complete entropy contraction from conditional hyperboundedness
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→ q hyperboundedness at time t0>0 combined with a GNS gap λ>0 implies a modified logarithmic Sobolev constant α=(λ(1−2/q))/(12(λt0+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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BibTeX
@misc{gao2026complete,
title = {{Complete entropy contraction from conditional hyperboundedness}},
author = {Li Gao and Lijun Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.35863},
eprint = {2610.35863},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.35863},
}
RIS
TY - UNPB
TI - Complete entropy contraction from conditional hyperboundedness
AU - Li Gao
AU - Lijun Wang
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.35863
UR - https://arxiv.org/abs/2610.35863
AB - 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→ q hyperboundedness at time t_0>0 combined with a GNS gap λ>0 implies a modified logarithmic Sobolev constant α=(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.
ER -