如何利用内存解释量子过程中的随机性
How much randomness in a quantum process can be explained using memory?
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中文总结 AI 辅助
该研究针对量子过程的随机性问题，利用Choi态表示构建平稳量子随机过程不可约随机性的收敛度量，为复制过程所需内存资源提供下界，推动量子类似方法发展。
中文摘要 AI 辅助
针对描述动力学系统观测结果的随机过程，复杂性科学提供了系统方法，可将产生的信息分解为真正不可约的随机性，以及看似随机实则可学习预测的结构。这些方法为系统内部结构的预测、控制和推断提供了重要工具。然而，由于侵入式测量和量子关联的固有复杂性，量子类似方法仍未充分发展。通过利用编码多时间输入输出关系的过程张量的Choi态表示，我们构建了平稳量子随机过程中不可约随机性的收敛度量，这直接实现了时间关联的度量，该度量为通过循环量子电路复制过程所需的内存资源设定了下界。
英文摘要
For a stochastic process describing observations of a dynamical system, complexity science provides systematic methods to decompose the information produced into true irreducible randomness, and that which corresponds to structure superficially disguised as random but can in fact be learned and predicted. Such methods then equip vital tools for prediction, control and inference of the system's internal structure. However, quantum analogs remain underdeveloped due to the inherent complications of invasive measurements and quantum correlations. By harnessing the Choi state representation of process tensors which encode multi-time input-output relations, we formulate a convergent measure of irreducible randomness in stationary quantum stochastic processes. This directly enables a measure of temporal correlations which lower bounds the memory resources required to replicate the process via a recurrent quantum circuit.
