Two-time expectation values of sequential measurements of dichotomic observables are known to be time symmetric for closed quantum systems. Namely, if a system evolves unitarily between sequential measurements of dichotomic observables $\mathscr{O}_{A}$ followed by $\mathscr{O}_{B}$, then it necessarily follows that $\langle\mathscr{O}_{A}\,,\mathscr{O}_{B}\rangle=\langle\mathscr{O}_{B}\,,\mathscr{O}_{A}\rangle$, where $\langle\mathscr{O}_{A}\,,\mathscr{O}_{B}\rangle$ is the two-time expectation value corresponding to the product of the measurement outcomes of $\mathscr{O}_{A}$ followed by $\mathscr{O}_{B}$, and $\langle\mathscr{O}_{B}\,,\mathscr{O}_{A}\rangle$ is the two-time expectation value associated with the time reversal of the unitary dynamics, where a measurement of $\mathscr{O}_{B}$ precedes a measurement of $\mathscr{O}_{A}$. In this work, we show that a quantum Bayes' rule implies a time symmetry for two-time expectation values associated with open quantum systems, which evolve according to a general quantum channel between measurements. Such results are in contrast with the view that processes associated with open quantum systems -- which may lose information to their environment -- are not reversible in any operational sense. We give an example of such time-symmetric correlations for the amplitude-damping channel, and we propose an experimental protocol for the potential verification of the theoretical predictions associated with our results.

翻译：已知对于封闭量子系统，二分可观测量序列测量的双时间期望值具有时间对称性。具体而言，若系统在二分可观测量$\mathscr{O}_{A}$与$\mathscr{O}_{B}$的连续测量之间经历幺正演化，则必有$\langle\mathscr{O}_{A}\,,\mathscr{O}_{B}\rangle=\langle\mathscr{O}_{B}\,,\mathscr{O}_{A}\rangle$成立，其中$\langle\mathscr{O}_{A}\,,\mathscr{O}_{B}\rangle$表示$\mathscr{O}_{A}$先于$\mathscr{O}_{B}$测量结果乘积对应的双时间期望值，而$\langle\mathscr{O}_{B}\,,\mathscr{O}_{A}\rangle$对应于时间反演的幺正动力学下$\mathscr{O}_{B}$先于$\mathscr{O}_{A}$测量的双时间期望值。本研究表明，量子贝叶斯规则意味着开放量子系统的双时间期望值同样具有时间对称性，这类系统在测量间遵循一般量子信道的演化规律。该结论与"开放量子系统（可能向环境泄露信息）在操作意义上不可逆"的传统观点形成对比。我们以振幅阻尼信道为例展示了此类时间对称关联，并提出了验证相关理论预测的实验方案。