Axioms for retrodiction: achieving time-reversal symmetry with a prior
We propose a category-theoretic definition of retrodiction and use it to exhibit a time-reversal symmetry for all quantum channels. We do this by introducing retrodiction families and functors, which capture many intuitive properties that retrodiction should satisfy and are general enough to encompa...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2023-05-01
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| Series: | Quantum |
| Online Access: | https://quantum-journal.org/papers/q-2023-05-23-1013/pdf/ |
| _version_ | 1797821856576700416 |
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| author | Arthur J. Parzygnat Francesco Buscemi |
| author_facet | Arthur J. Parzygnat Francesco Buscemi |
| author_sort | Arthur J. Parzygnat |
| collection | DOAJ |
| description | We propose a category-theoretic definition of retrodiction and use it to exhibit a time-reversal symmetry for all quantum channels. We do this by introducing retrodiction families and functors, which capture many intuitive properties that retrodiction should satisfy and are general enough to encompass both classical and quantum theories alike. Classical Bayesian inversion and all rotated and averaged Petz recovery maps define retrodiction families in our sense. However, averaged rotated Petz recovery maps, including the universal recovery map of Junge-Renner-Sutter-Wilde-Winter, do not define retrodiction functors, since they fail to satisfy some compositionality properties. Among all the examples we found of retrodiction families, the original Petz recovery map is the only one that defines a retrodiction functor. In addition, retrodiction functors exhibit an inferential time-reversal symmetry consistent with the standard formulation of quantum theory. The existence of such a retrodiction functor seems to be in stark contrast to the many no-go results on time-reversal symmetry for quantum channels. One of the main reasons is because such works defined time-reversal symmetry on the category of quantum channels alone, whereas we define it on the category of quantum channels and quantum states. This fact further illustrates the importance of a prior in time-reversal symmetry. |
| first_indexed | 2024-03-13T09:58:58Z |
| format | Article |
| id | doaj.art-b0724d247eb3455982a11d4dc99e0540 |
| institution | Directory Open Access Journal |
| issn | 2521-327X |
| language | English |
| last_indexed | 2024-03-13T09:58:58Z |
| publishDate | 2023-05-01 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | Article |
| series | Quantum |
| spelling | doaj.art-b0724d247eb3455982a11d4dc99e05402023-05-23T10:31:23ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2023-05-017101310.22331/q-2023-05-23-101310.22331/q-2023-05-23-1013Axioms for retrodiction: achieving time-reversal symmetry with a priorArthur J. ParzygnatFrancesco BuscemiWe propose a category-theoretic definition of retrodiction and use it to exhibit a time-reversal symmetry for all quantum channels. We do this by introducing retrodiction families and functors, which capture many intuitive properties that retrodiction should satisfy and are general enough to encompass both classical and quantum theories alike. Classical Bayesian inversion and all rotated and averaged Petz recovery maps define retrodiction families in our sense. However, averaged rotated Petz recovery maps, including the universal recovery map of Junge-Renner-Sutter-Wilde-Winter, do not define retrodiction functors, since they fail to satisfy some compositionality properties. Among all the examples we found of retrodiction families, the original Petz recovery map is the only one that defines a retrodiction functor. In addition, retrodiction functors exhibit an inferential time-reversal symmetry consistent with the standard formulation of quantum theory. The existence of such a retrodiction functor seems to be in stark contrast to the many no-go results on time-reversal symmetry for quantum channels. One of the main reasons is because such works defined time-reversal symmetry on the category of quantum channels alone, whereas we define it on the category of quantum channels and quantum states. This fact further illustrates the importance of a prior in time-reversal symmetry.https://quantum-journal.org/papers/q-2023-05-23-1013/pdf/ |
| spellingShingle | Arthur J. Parzygnat Francesco Buscemi Axioms for retrodiction: achieving time-reversal symmetry with a prior Quantum |
| title | Axioms for retrodiction: achieving time-reversal symmetry with a prior |
| title_full | Axioms for retrodiction: achieving time-reversal symmetry with a prior |
| title_fullStr | Axioms for retrodiction: achieving time-reversal symmetry with a prior |
| title_full_unstemmed | Axioms for retrodiction: achieving time-reversal symmetry with a prior |
| title_short | Axioms for retrodiction: achieving time-reversal symmetry with a prior |
| title_sort | axioms for retrodiction achieving time reversal symmetry with a prior |
| url | https://quantum-journal.org/papers/q-2023-05-23-1013/pdf/ |
| work_keys_str_mv | AT arthurjparzygnat axiomsforretrodictionachievingtimereversalsymmetrywithaprior AT francescobuscemi axiomsforretrodictionachievingtimereversalsymmetrywithaprior |