论文标题
在Unital Quantum Markov Semigroups下的自限制噪声和指数相对熵衰减
Self-restricting Noise and Exponential Relative Entropy Decay Under Unital Quantum Markov Semigroups
论文作者
论文摘要
在环境相互作用下，开放量子系统的状态通常会连续衰减。 Markov Semigroups在耗散环境中模拟此类过程。众所周知，具有GNS详细平衡的有限维量子Markov半群，普遍遵守完整的修改的对数Sobolev不等式（CMLSIS），从而产生了固定点状态下一个子空间的相对熵的指数衰减。我们分析了将耗散性与哈密顿时间进化相结合的连续过程，从而排除了这种详细平衡的概念。首先，我们为这些过程发现了类似CMLSI的衰减的反例，并确定其失败的条件。相比之下，我们证明，尽管在早期缺席，但在有限的时间尺度上的Unital，有限维量子Markov Semigroups的指数衰减重新出现。最后，我们表明，当耗散比哈密顿的时间进化强得多时，对半群的无腐烂子空间的最终，指数衰减的速率在单独的耗散部分的衰减速率上成反比。当强阻尼抑制效果时，这种反相关关系被称为自限制的噪声，否则噪音将超出其初始子空间。
States of open quantum systems often decay continuously under environmental interactions. Quantum Markov semigroups model such processes in dissipative environments. It is known that finite-dimensional quantum Markov semigroups with GNS detailed balance universally obey complete modified logarithmic Sobolev inequalities (CMLSIs), yielding exponential decay of relative entropy to a subspace of fixed point states. We analyze continuous processes that combine dissipative with Hamiltonian time-evolution, precluding this notion of detailed balance. First, we find counterexamples to CMLSI-like decay for these processes and determine conditions under which it fails. In contrast, we prove that despite its absence at early times, exponential decay re-appears for unital, finite-dimensional quantum Markov semigroups at finite timescales. Finally, we show that when dissipation is much stronger than Hamiltonian time-evolution, the rate of eventual, exponential decay toward the semigroup's decoherence-free subspace is bounded inversely in the decay rate of the dissipative part alone. Dubbed self-restricting noise, this inverse relationship arises when strong damping suppresses effects that would otherwise spread noise beyond its initial subspace.
