Computation of sandwiched relative alpha-entropy of two n-mode gaussian states

Abstract

A formula for the sandwiched relative $\alpha$-entropy ${\tilde{D}}_{\alpha }(\rho ||\sigma )=\frac{1}{\alpha -1}\ln \mathrm{Tr}{\left({\sigma }^{\frac{1-\alpha }{2\alpha }}\rho {\sigma }^{\frac{1-\alpha }{2\alpha }}\right)}^{\alpha }$ for $0<\alpha <1$, of two $n$ mode gaussian states $\rho$, $\sigma$ in the boson Fock space $\Gamma ({\mathbb{C}}^n)$ is presented. This computation extensively employs the ${\mathcal{E}}_2$-parametrization of gaussian states in $\Gamma ({\mathbb{C}}^n)$ introduced in J. Math. Phys. {\bf 62} (2021), 022102.

arXiv comment11 pages, no figures

References in corpus (4)

• Strong converse for the classical capacity of entanglement-breaking and Hadamard channels via a sandwiched Renyi relative entropy
• Quantum hypothesis testing and the operational interpretation of the quantum Renyi relative entropies
• Correlation Detection and an Operational Interpretation of the Renyi Mutual Information
• A pedagogical note on the computation of relative entropy of two $n$-mode gaussian states