Gier David, Crutchfield James P
Complexity Sciences Center and Physics and Astronomy Department, University of California at Davis, One Shields Avenue, Davis, CA 95616, USA.
Entropy (Basel). 2025 Jun 3;27(6):599. doi: 10.3390/e27060599.
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.
静止量子信息源发射相关量子位序列，即结构化量子随机过程。如果观察者对量子位序列进行相同的测量，其结果就是一个经典随机过程的实现。我们引入了可分量子位序列的量子信息理论性质，这些性质可作为后续测量过程经典信息性质的界限。对于由隐马尔可夫动力学驱动的源，我们描述了观察者如何使用特定的正算子值测量或自适应测量协议暂时或永久同步到源的内部状态。我们通过断层重建引入了一种用独立同分布、马尔可夫或更大记忆模型逼近信息源的方法。我们根据可分过程的量子信息性质以及同步和精确重建它们所需测量的复杂性，确定了广泛的可分过程类别。
