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- W4323572068 abstract "In this article, we obtain the precise range of the values of the parameter $alpha$ such that Petz-R'enyi $alpha$-relative entropy $D_{alpha}(rho||sigma)$ of two displaced thermal states is finite. More precisely, we prove that, given two displaced thermal states $rho$ and $sigma$ with inverse temperature parameters $r_1, r_2,dots, r_n$ and $s_1,s_2, dots, s_n$, respectively, we have [ D_{alpha}(rho||sigma)<infty Leftrightarrow alpha < min left{ frac{s_j}{s_j-r_j}: j in { 1, ldots , n } text{ such that } r_j<s_j right}, ] where we adopt the convention that the minimum of an empty set is equal to infinity. Along the way, we prove a special case of a conjecture of Seshdreesan, Lami and Wilde (J. Math. Phys. 59, 072204 (2018))." @default.
- W4323572068 created "2023-03-09" @default.
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- W4323572068 date "2023-03-06" @default.
- W4323572068 modified "2023-09-23" @default.
- W4323572068 title "Petz-R'enyi Relative Entropy of Thermal States and their Displacements" @default.
- W4323572068 doi "https://doi.org/10.48550/arxiv.2303.03380" @default.
- W4323572068 hasPublicationYear "2023" @default.
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