发表机构
Nagoya University（名古屋大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明量子贝叶斯逆推可产生与任何经典贝叶斯学习不相容的预测，且五结果测量即突破经典界限，展示其更强的表达力。
AI 中文摘要
一个智能体的预测能否揭示其推理是基于经典模型还是量子模型？利用矩阵分解的已知结果，我们在此表明，量子贝叶斯逆推可以产生一步前瞻预测，这些预测与基于条件独立观测学习固定但未知采样律的每一种经典贝叶斯解释都不相容。这种分离在结果数量上存在一个尖锐阈值：对于任何最多四个结果的测量，无论先验状态和有限希尔伯特空间维度如何，量子预测都允许经典实现，而单量子比特上的五结果测量已经违反了一个明确的经典界限。该界限对任意经典隐状态、先验概率和采样律均成立，并且仅涉及智能体的初始和更新预测。因此，在这种设定下，量子贝叶斯逆推严格比经典贝叶斯学习更具表达力，并且这种差异可以在不观察或指定智能体内部描述的情况下被见证。
英文摘要
Can an agent's predictions reveal whether its reasoning is based on a classical or a quantum model? Using known results on matrix factorizations, here we show that quantum Bayesian retrodiction can produce one-step-ahead forecasts incompatible with every classical Bayesian explanation based on learning about a fixed but unknown sampling law from conditionally independent observations. The separation has a sharp threshold in the number of outcomes: for any measurement with at most four outcomes, the quantum predictions admit a classical realization, irrespective of the prior state and the finite Hilbert-space dimension, whereas a five-outcome measurement on a single qubit already violates an explicit classical bound. This bound holds for arbitrary classical latent states, prior probabilities, and sampling laws, and involves only the agent's initial and updated predictions. Thus, in this setting, quantum Bayesian retrodiction is strictly more expressive than classical Bayesian learning, and this difference can be witnessed without observing or specifying the agent's internal description.
Commentsv2: discussion expanded, bound added; v1: 4 pages, one diagram
