Stationary quantum information sources emit sequences of correlated qudits -- that is, structured quantum stochastic processes. If an observer performs identical measurements on a qudit sequence, the outcomes are a realization of a classical stochastic process. We introduce quantum-information-theoretic properties for separable qudit sequences that serve as bounds on the classical information properties of subsequent measured processes. For sources driven by hidden Markov dynamics we describe how an observer can temporarily or permanently synchronize to the source's internal state using specific positive operator-valued measures or adaptive measurement protocols. We introduce a method for approximating an information source with an independent and identically-distributed, Markov, or larger memory model through tomographic reconstruction. We identify broad classes of separable processes based on their quantum information properties and the complexity of measurements required to synchronize to and accurately reconstruct them.

翻译：稳态量子信息源发射出相互关联的量子比特序列——即结构化的量子随机过程。若观察者对量子比特序列进行相同测量，其结果会表现为经典随机过程的实现。我们引入可分量子比特序列的量子信息论性质，这些性质可作为后续测量过程经典信息性质的界。对于由隐马尔可夫动力学驱动的信息源，我们描述了观察者如何通过特定正算子值测量或自适应测量协议，暂时或永久地同步至信息源的内部状态。我们提出一种方法，利用层析重建将信息源近似为独立同分布、马尔可夫或更大记忆模型。我们根据可分过程的量子信息性质以及为实现同步与精确重建所需测量的复杂度，识别出宽广的可分过程类别。