In 1976, Gorini, Kossakowski, Sudarshan and Lindblad independently discovered a general form of master equations for an open quantum Markovian dynamics. In honor of all the authors, the equation is nowadays called the GKLS master equation. In this paper, we show universal constraints on the relaxation times valid for any d-level GKLS master equations, which is a generalization of the well-known constraints for 2-level systems. Specifically, we show that any relaxation rate, the inverse-relaxation time, is not greater than half of the sum of all relaxation rates. Since the relaxation times are measurable in experiments, our constraints provide a direct experimental test for the validity of the GKLS master equations, and hence for the conditions of the complete positivity and Markovianity.

中文翻译：

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d-Level GKLS 主方程松弛时间的通用约束

1976 年，Gorini、Kossakowski、Sudarshan 和 Lindblad 独立发现了开放量子马尔可夫动力学的一般形式的主方程。为了纪念所有作者，这个方程现在被称为 GKLS 主方程。在本文中，我们展示了对任何 d 级 GKLS 主方程有效的松弛时间的通用约束，这是对 2 级系统的众所周知的约束的推广。具体来说，我们表明任何弛豫率，即反弛豫时间，不大于所有弛豫率之和的一半。由于松弛时间在实验中是可测量的，我们的约束为 GKLS 主方程的有效性提供了直接的实验测试，因此也为完全正性和马尔可夫的条件提供了直接的实验测试。