超越细致平衡的紧熵收缩
Tight entropy contraction beyond detailed balance
- School of Mathematics and Statistics, Wuhan University（武汉大学数学与统计学院）
- Wuhan Institute of Quantum Technology（武汉量子技术研究院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文为有限维量子信道建立超越细致平衡的紧熵收缩界，通过GNS范数收缩导出相对熵收缩，并应用于量子马尔可夫半群，给出完全修正对数Sobolev常数的下界，且允许外部环境纠缠，所得界具有最优尺寸依赖。
AI中文摘要：
我们为有限维量子信道建立了超越细致平衡的定量熵收缩界。对于与忠实条件期望相容的信道，我们证明GNS（Gelfand--Naimark--Segal）范数收缩仅在对数维度常数损失下即可导出相对熵收缩。对于具有忠实渐近条件期望的量子马尔可夫半群，这给出了基于GNS谱隙的完全修正对数Sobolev常数的下界。这些界允许与外部环境的初始纠缠，且独立于其系统大小。应用于交替储层脉冲和连续耦合能量梯级时，所得界具有最优的尺寸依赖关系。
英文摘要：
We establish quantitative entropy contraction bounds for finite-dimensional quantum channels beyond detailed balance. For channels compatible with a faithful conditional expectation, we show that GNS (Gelfand--Naimark--Segal) norm contraction yields relative entropy contraction with only a logarithmic loss in the dimensional constant. For quantum Markov semigroups with a faithful asymptotic conditional expectation, this gives a lower bound on the complete modified logarithmic Sobolev constant in terms of the GNS spectral gap. The bounds allow initial entanglement with an external environment and are independent of its system size. Applications to alternating reservoir pulses and continuously coupled energy ladders give bounds with optimal size dependence.
