We consider quantum stochastic processes and discuss a level 2.5 large deviation formalism providing an explicit and complete characterisation of fluctuations of time-averaged quantities, in the large-time limit. We analyse two classes of quantum stochastic dynamics, within this framework. The first class consists of the quantum jump trajectories related to photon detection; the second is quantum state diffusion related to homodyne detection. For both processes, we present the level 2.5 functional starting from the corresponding quantum stochastic Schrödinger equation and we discuss connections of these functionals to optimal control theory.

中文翻译：

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马尔可夫开放量子系统的 2.5 级大偏差：量子跳跃和量子态扩散

我们考虑了量子随机过程并讨论了 2.5 级大偏差形式主义，它在大时间限制内提供了时间平均量波动的明确和完整的表征。我们在这个框架内分析了两类量子随机动力学。第一类包括与光子探测相关的量子跳跃轨迹；第二个是与零差检测相关的量子态扩散。对于这两个过程，我们从相应的量子随机薛定谔方程开始提出 2.5 级泛函，并讨论这些泛函与最优控制理论的联系。