Observational entropy captures both the intrinsic uncertainty of a thermodynamic state and the lack of knowledge due to coarse-graining. We demonstrate two interpretations of observational entropy, one as the statistical deficiency resulting from a measurement, the other as the difficulty of inferring the input state from the measurement statistics by quantum Bayesian retrodiction. These interpretations show that the observational entropy implicitly includes a uniform reference prior. Since the uniform prior cannot be used when the system is infinite-dimensional or otherwise energy-constrained, we propose generalizations by replacing the uniform prior with arbitrary quantum states that may not even commute with the state of the system. We propose three candidates for this generalization, discuss their properties, and show that one of them gives a unified expression that relates both interpretations.

中文翻译：

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具有一般量子先验的观测熵


观测熵既捕获了热力学状态的内在不确定性，也捕获了由于粗粒度而导致的知识缺乏。我们展示了对观测熵的两种解释，一种是测量导致的统计缺陷，另一种是通过量子贝叶斯逆移从测量统计中推断输入状态的困难。这些解释表明，观测熵隐含地包括一个统一的参考先验。由于当系统是无限维的或其他能量约束时，不能使用统一先验，因此我们提出了泛化，将统一先验替换为任意量子态，这些量子态甚至可能无法与系统的状态交换。我们为这种概括提出了三个候选者，讨论了它们的性质，并表明其中一个给出了将两种解释联系起来的统一表达式。