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arXiv · 2109.04062

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

K R Parthasarathy
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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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K R Parthasarathy. 2021-09-09. Computation of sandwiched relative alpha-entropy of two n-mode gaussian states. https://arxiv.org/abs/2109.04062

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