English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

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. Moreprecisely, 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 toinfinity. Along the way, we prove a special case of a conjecture ofSeshdreesan, Lami and Wilde (J. Math. Phys. 59, 072204 (2018)).

Petz-R\'enyi Relative Entropy of Thermal States and their Displacements