Observational entropy, coarse-grained states, and the Petz recovery map: information-theoretic properties and bounds
Observational entropy provides a general notion of quantum entropy that appropriately interpolates between Boltzmann’s and Gibbs’ entropies, and has recently been argued to provide a useful measure of out-of-equilibrium thermodynamic entropy. Here we study the mathematical properties of observationa...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2023-01-01
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| Series: | New Journal of Physics |
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| Online Access: | https://doi.org/10.1088/1367-2630/accd11 |
| _version_ | 1797748660266598400 |
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| author | Francesco Buscemi Joseph Schindler Dominik Šafránek |
| author_facet | Francesco Buscemi Joseph Schindler Dominik Šafránek |
| author_sort | Francesco Buscemi |
| collection | DOAJ |
| description | Observational entropy provides a general notion of quantum entropy that appropriately interpolates between Boltzmann’s and Gibbs’ entropies, and has recently been argued to provide a useful measure of out-of-equilibrium thermodynamic entropy. Here we study the mathematical properties of observational entropy from an information-theoretic viewpoint, making use of recently strengthened forms of the monotonicity property of quantum relative entropy. We present new bounds on observational entropy applying in general, as well as bounds and identities related to sequential and post-processed measurements. A central role in this work is played by what we call the ‘coarse-grained’ state, which emerges from the measurement’s statistics by Bayesian retrodiction, without presuming any knowledge about the ‘true’ underlying state being measured. The degree of distinguishability between such a coarse-grained state and the true (but generally unobservable) one is shown to provide upper and lower bounds on the difference between observational and von Neumann entropies. |
| first_indexed | 2024-03-12T16:08:57Z |
| format | Article |
| id | doaj.art-d55fe067dd3d4001a0cabc227128f429 |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:08:57Z |
| publishDate | 2023-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-d55fe067dd3d4001a0cabc227128f4292023-08-09T14:15:19ZengIOP PublishingNew Journal of Physics1367-26302023-01-0125505300210.1088/1367-2630/accd11Observational entropy, coarse-grained states, and the Petz recovery map: information-theoretic properties and boundsFrancesco Buscemi0https://orcid.org/0000-0001-9741-0628Joseph Schindler1https://orcid.org/0000-0002-8799-9800Dominik Šafránek2https://orcid.org/0000-0002-6861-395XDepartment of Mathematical Informatics, Nagoya University, Furo-cho , Chikusa-ku 464-8601 JapanFísica Teòrica: Informació i Fenòmens Quàntics, Departament de Física, Universitat Autònoma de Barcelona , 08193 Bellaterra, SpainCenter for Theoretical Physics of Complex Systems, Institute for Basic Science (IBS) , Daejeon 34126, Republic of KoreaObservational entropy provides a general notion of quantum entropy that appropriately interpolates between Boltzmann’s and Gibbs’ entropies, and has recently been argued to provide a useful measure of out-of-equilibrium thermodynamic entropy. Here we study the mathematical properties of observational entropy from an information-theoretic viewpoint, making use of recently strengthened forms of the monotonicity property of quantum relative entropy. We present new bounds on observational entropy applying in general, as well as bounds and identities related to sequential and post-processed measurements. A central role in this work is played by what we call the ‘coarse-grained’ state, which emerges from the measurement’s statistics by Bayesian retrodiction, without presuming any knowledge about the ‘true’ underlying state being measured. The degree of distinguishability between such a coarse-grained state and the true (but generally unobservable) one is shown to provide upper and lower bounds on the difference between observational and von Neumann entropies.https://doi.org/10.1088/1367-2630/accd11observational entropyPetz mapcoarse quantum statesquantum relative entropystate inference |
| spellingShingle | Francesco Buscemi Joseph Schindler Dominik Šafránek Observational entropy, coarse-grained states, and the Petz recovery map: information-theoretic properties and bounds New Journal of Physics observational entropy Petz map coarse quantum states quantum relative entropy state inference |
| title | Observational entropy, coarse-grained states, and the Petz recovery map: information-theoretic properties and bounds |
| title_full | Observational entropy, coarse-grained states, and the Petz recovery map: information-theoretic properties and bounds |
| title_fullStr | Observational entropy, coarse-grained states, and the Petz recovery map: information-theoretic properties and bounds |
| title_full_unstemmed | Observational entropy, coarse-grained states, and the Petz recovery map: information-theoretic properties and bounds |
| title_short | Observational entropy, coarse-grained states, and the Petz recovery map: information-theoretic properties and bounds |
| title_sort | observational entropy coarse grained states and the petz recovery map information theoretic properties and bounds |
| topic | observational entropy Petz map coarse quantum states quantum relative entropy state inference |
| url | https://doi.org/10.1088/1367-2630/accd11 |
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