广义量子退极化的紧熵收缩
Tight Entropy Contraction of Generalized Quantum Depolarization
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中文总结 AI 辅助
该研究建立了广义量子退极化信道及半群相对熵收缩的上下界，给出收缩率的紧一阶渐近行为，结果可推广至乘积动力学，对相干性与非对称性衰减率有重要意义。
中文摘要 AI 辅助
我们建立了广义量子退极化信道及半群的相对熵收缩的上下界。该界给出了收缩率关于维数常数的紧一阶渐近行为。一侧估计基于两态相对熵的尖锐反向比率与凸性，可由新近提出的 Hockey-Stick 量子 f-散度导出，也可独立通过 Bogoliubov-Kubo-Mori 量子费舍尔信息度量得到；另一侧则基于关于一般条件期望的指标达到纯态的存在性。我们的结果可推广至完全熵收缩率、乘积动力学的张量稳定估计，实例包括量子退极化、退相位及紧群对称化，对相干性与非对称性的衰减率具有重要意义。
英文摘要
We establish upper and lower bounds for relative entropy contraction of generalized quantum depolarizing channels and semigroups. Our bound provides tight first order asymptotic of the contraction rate in terms of the dimension constant. One side estimate are based on sharp reverse ratio and convexity of relative entropy of two states, which can be derived from the recently introduced Hockey-Stick quantum $f$-divergence, and also independently, Bogoliubov--Kubo--Mori quantum Fisher information metric. The other side follows from the existence of index achieving pure state with respect to a general conditional expectation. Our results extend to the complete entropy contraction rate, tensor stable estimates for product dynamics. Examples include quantum depolarization, dephasing, and compact group symmetrization, with consequences for the decay rate of coherence and asymmetry.
