论文标题
测得的量子态随机过程的最佳和复杂性
Optimality and Complexity in Measured Quantum-State Stochastic Processes
论文作者
论文摘要
如果实验学家通过投影或正操作员值测量观察一系列发射的量子状态，则结果形成时间序列。单个时间序列是对测量结果的随机过程的实现。我们最近表明，总的来说，所得的随机过程在两个特定的感觉上是高度复杂的：（i）在不同程度上，它本质上是不可预测的，它取决于测量选择，并且（ii）最佳预测需要使用无限数量的时间特征。在这里，我们将这种复杂性的基础机制确定为发电机不可分性 - 发电机状态序列与测量结果序列之间的脱落性。这可以定量探讨测量选择对量子过程的随机性和结构复杂性的影响，使用厄尔及义理论最近引入的方法。但是，在此过程中，需要定量的结构和记忆时间序列中的定量度量。而且，成功需要准确有效的估计算法，这些算法克服了明确表示无限的预测特征的要求。我们提供这些指标和相关算法，使用它们来设计开放量子动力学系统的信息最佳测量。
If an experimentalist observes a sequence of emitted quantum states via either projective or positive-operator-valued measurements, the outcomes form a time series. Individual time series are realizations of a stochastic process over the measurements' classical outcomes. We recently showed that, in general, the resulting stochastic process is highly complex in two specific senses: (i) it is inherently unpredictable to varying degrees that depend on measurement choice and (ii) optimal prediction requires using an infinite number of temporal features. Here, we identify the mechanism underlying this complicatedness as generator nonunifilarity -- the degeneracy between sequences of generator states and sequences of measurement outcomes. This makes it possible to quantitatively explore the influence that measurement choice has on a quantum process' degrees of randomness and structural complexity using recently introduced methods from ergodic theory. Progress in this, though, requires quantitative measures of structure and memory in observed time series. And, success requires accurate and efficient estimation algorithms that overcome the requirement to explicitly represent an infinite set of predictive features. We provide these metrics and associated algorithms, using them to design informationally-optimal measurements of open quantum dynamical systems.
