提出统一比较量子与经典模型的方法，揭示生成随机过程的最小量子尺寸
Identifiability and minimality bounds of quantum and post-quantum models of classical stochastic processes
- 将各类模型映射到通用隐马尔可夫框架，实现跨模型可比性
- 给出量子模型生成特定过程所需的最小维度上界，部分情况为紧界
- 适用于研究量子优势、信息压缩及非经典资源的理论边界
为理解周围世界，我们构建模型以复现、描述和解释所见行为。针对相关随机变量序列（即经典随机过程）这一广泛情形，本文解决两个不同模型是否产生相同可观测行为的问题，即可辨识性问题。值得注意的是，模型物理机制无需与观测物理一致；近期研究表明，使用量子模型生成经典随机过程在内存与热效率上更具优势。本文在该范式下解决了可辨识性问题，通过将任意模型（经典、量子或后量子）映射至一个规范化的‘广义’隐马尔可夫模型，实现对任意两模型的比较。此外，该方法使我们能对生成给定经典随机过程所需的最小量子模型维度进行（有时是紧致的）约束。
原文摘要 · Abstract (English)
To make sense of the world around us, we develop models, constructed to enable us to replicate, describe, and explain the behaviours we see. Focusing on the broad case of sequences of correlated random variables, i.e., classical stochastic processes, we tackle the question of determining whether or not two different models produce the same observable behavior. This is the problem of identifiability. Curiously, the physics of the model need not correspond to the physics of the observations; recent work has shown that it is even advantageous -- in terms of memory and thermal efficiency -- to employ quantum models to generate classical stochastic processes. We resolve the identifiability problem in this regime, providing a means to compare any two models of a classical process, be the models classical, quantum, or `post-quantum', by mapping them to a canonical `generalized' hidden Markov model. Further, this enables us to place (sometimes tight) bounds on the minimal dimension required of a quantum model to generate a given classical stochastic process.
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