发表机构
University of Manchester（曼彻斯特大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出全量子计算力学框架，证明平稳有记忆量子空间序列可由记忆最小模型等距生成，其最小记忆熵等于纠缠熵，并建立零基本熵率与无限量子马尔可夫阶，揭示因果生成与量子复杂性的深层联系。
AI 中文摘要
是什么让一个量子过程比另一个更复杂？我们采用一种受经典复杂性科学启发的操作性方法，该方法通过因果生成所需的记忆来刻画结构。我们为量子空间序列开发了计算力学的全量子扩展：即不返回与其生成器相互作用的量子输出序列。对于允许有限维、本原因果模型的平稳、有记忆的量子空间序列，我们证明可以选择一个记忆最小模型来等距地生成输出，而无需丢弃环境。由此产生的典型矩阵乘积态表示同时确定了最小记忆维度和最小记忆熵。后者恰好是过去-未来二分上的纠缠熵，从而赋予纠缠一种操作性解释，即作为因果生成中不可约的记忆。在这一类中，我们进一步建立了消失的基本熵率、因果不对称性的缺失以及无限的量子马尔可夫阶。这些结果建立了一个用于量化内在量子结构的操作性框架，揭示了因果生成、复杂性、记忆、熵和纠缠之间的深层联系。
英文摘要
What makes one quantum process more complex than another? We adopt an operational approach inspired by classical complexity science, which characterises structure through the memory required for causal generation. We develop a fully-quantum extension of computational mechanics for quantum space series: Sequences of quantum outputs that do not return to interact with their generator. For stationary, memoryful quantum space series admitting finite-dimensional, primitive causal models, we show that a memory-minimal model can be chosen to generate the outputs isometrically, without a discarded environment. The resulting canonical matrix product state representation determines both the minimum memory dimension and the minimum memory entropy. The latter is precisely the entanglement entropy across the past-future bipartition, giving entanglement an operational interpretation as irreducible memory for causal generation. Within this class, we further establish a vanishing fundamental entropy rate, the absence of causal asymmetry, and infinite quantum Markov order. These results establish an operational framework for quantifying intrinsic quantum structure, revealing deep connections between causal generation, complexity, memory, entropy, and entanglement.
Comments15 pages, 2 figures
