Universal Constraint for Relaxation Rates for Quantum Dynamical Semigroup,Physical Review Letters

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Universal Constraint for Relaxation Rates for Quantum Dynamical Semigroup
Physical Review Letters ( IF 8.1 ) Pub Date : 2021-07-30 , DOI: 10.1103/physrevlett.127.050401
Dariusz Chruściński ₁ , Gen Kimura ₂ , Andrzej Kossakowski ₁ , Yasuhito Shishido ₂

Affiliation

A general property of relaxation rates in open quantum systems is discussed. We find an interesting constraint for relaxation rates that universally holds in fairly large classes of quantum dynamics, e.g., weak coupling regimes, as well as for entropy nondecreasing evolutions. We conjecture that this constraint is universal, i.e., it is valid for all quantum dynamical semigroups. The conjecture is supported by numerical analysis. Moreover, we show that the conjectured constraint is tight by providing a concrete model that saturates the bound. This universality marks an essential step toward the physical characterization of complete positivity as the constraint is directly verifiable in experiments. It provides, therefore, a physical manifestation of complete positivity. Our conjecture also has two important implications: it provides (i) a universal constraint for the spectra of quantum channels and (ii) a necessary condition to decide whether a given channel is consistent with Markovian evolution.

中文翻译：

量子动力学半群弛豫率的普遍约束

讨论了开放量子系统中弛豫率的一般性质。我们发现了一个有趣的弛豫率约束，它普遍适用于相当大类的量子动力学，例如弱耦合机制，以及熵非递减演化。我们推测这个约束是普遍的，即它对所有量子动力学半群都有效。该猜想得到了数值分析的支持。此外，我们通过提供一个使边界饱和的具体模型来证明推测的约束是严格的。这种普遍性标志着朝着完全阳性的物理特征迈出的重要一步，因为约束可以在实验中直接验证。因此，它提供了完全积极的身体表现。我们的猜想还有两个重要的含义：

更新日期：2021-07-30

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