We determine the conditions for the equivalence between the multi-time expectation values of a general finite-dimensional open quantum system when interacting with, respectively, an environment undergoing a free unitary evolution or a discrete environment under a free evolution fixed by a proper Gorini-Kossakowski-Lindblad-Sudarshan generator. We prove that the equivalence holds if both environments are bosonic and Gaussian and if the one- and two-time correlation functions of the corresponding interaction operators are the same at all times. This result leads to a non-perturbative evaluation of the multi-time expectation values of operators and maps of open quantum systems interacting with a continuous set of bosonic modes by means of a limited number of damped modes, thus setting the ground for the investigation of open-system multi-time quantities in fully general regimes.

我们确定了一般有限维开放量子系统的多次期望值在分别与经历自由酉演化的环境或由适当的 Gorini- 固定的自由演化下的离散环境相互作用时的等价条件Kossakowski-Lindblad-Sudarshan 发电机。我们证明，如果两种环境都是玻色子和高斯环境，并且相应交互算子的一次和二次相关函数始终相同，则等价性成立。该结果导致对运算符的多次期望值和开放量子系统的映射的非微扰评估通过有限数量的阻尼模式与一组连续的玻色子模式相互作用，