Petz–Rényi relative entropy of thermal states and their displacements
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2303.03380v2.pdf
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Final Accepted Manuscript
Affiliation
The University of ArizonaIssue Date
2024-04-17Keywords
Gaussian statesNussbaum–Szkoła distributions
Petz–Rényi α-relative entropy
Primary 81P17
Quantum relative entropy
Secondary 81P99
Thermal states
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Springer Science and Business Media LLCCitation
Androulakis, G., John, T.C. Petz–Rényi relative entropy of thermal states and their displacements. Lett Math Phys 114, 57 (2024). https://doi.org/10.1007/s11005-024-01805-zJournal
Letters in Mathematical PhysicsRights
©TheAuthor(s), under exclusive licence to Springer Nature B.V. 2024.Collection Information
This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at repository@u.library.arizona.edu.Abstract
In this letter, we obtain the precise range of the values of the parameter α such that Petz–Rényi α-relative entropy Dα(ρ||σ) of two faithful displaced thermal states is finite. More precisely, we prove that, given two displaced thermal states ρ and σ with inverse temperature parameters r1,r2,…,rn and s1,s2,…,sn, respectively, 0<rj,sj<∞, for all j, we have (Formula presented.) where we adopt the convention that the minimum of an empty set is equal to infinity. This result is particularly useful in the light of operational interpretations of the Petz–Rényi α-relative entropy in the regime α>1. Along the way, we also prove a special case of a conjecture of Seshadreesan et al. (J Math Phys 59(7):072204, 2018. https://doi.org/10.1063/1.5007167).Note
12 month embargo; first published 17 April 2024EISSN
1573-0530Version
Final accepted manuscriptSponsors
Multidisciplinary University Research Initiativeae974a485f413a2113503eed53cd6c53
10.1007/s11005-024-01805-z