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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2023
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2308.08763 |
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| _version_ | 1866910704732209152 |
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| author | Bai, Ge Šafránek, Dominik Schindler, Joseph Buscemi, Francesco Scarani, Valerio |
| author_facet | Bai, Ge Šafránek, Dominik Schindler, Joseph Buscemi, Francesco Scarani, Valerio |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_08763 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Observational entropy with general quantum priors Bai, Ge Šafránek, Dominik Schindler, Joseph Buscemi, Francesco Scarani, Valerio Quantum Physics 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. |
| title | Observational entropy with general quantum priors |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2308.08763 |