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

• URL: http://arxiv.org/abs/2109.04062v2
• Date: Fri, 12 Nov 2021 04:01:08 GMT
• Title: Computation of sandwiched relative alpha-entropy of two n-mode gaussian states
• Authors: K R Parthasarathy
• Abstract summary: formula for sandwiched relative $alpha$-entropy $widetildeD_alpha(rhovertvertsigma)=frac1alpha-1, ln,rm Tr, left(sigmafrac1-alpha2alpha,rho,sigmafrac1-alpha2alpharight)alpha for $0 alpha 1$, of two $n$ mode rhogaussian states $mathbbCn
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: A formula for the sandwiched relative $\alpha$-entropy $\widetilde{D}_\alpha(\rho\vert\vert\sigma)=\frac{1}{\alpha-1}\, \ln\,{\rm Tr}\, \left(\sigma^{\frac{1-\alpha}{2\alpha}}\,\rho\,\sigma^{\frac{1-\alpha}{2\alpha}}\right)^\alpha$ 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.

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