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Published at November 29

Reverse-type Data Processing Inequality

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Released Date: November 29, 2024

Authors: Paula Belzig¹, Li Gao², Graeme Smith¹, Peixue Wu¹

Aff.: ¹Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, Canada; ²School of Mathematics and Statistics, Wuhan University, Wuhan, Hubei, China

Arxiv: http://arxiv.org/pdf/2411.19890v1

Channels $(\mathcal{N},\mathcal{M})$	Upper bound for $\eta_{\mathcal{N},\mathcal{M}}$	Lower bound for $\widecheck{\eta}_{\mathcal{N},\mathcal{M}}$
Depolarizing: $(\mathcal{D}_{p_{1}},\mathcal{D}_{p_{2}})$	$\left(\frac{1-p_{1}}{1-p_{2}}\right)^{2}\frac{1-\frac{d-1}{d}p_{2}}{1-\frac{d-% 1}{d}p_{1}}$	$\left(\frac{1-p_{1}}{1-p_{2}}\right)^{2}\frac{p_{2}}{p_{1}}$
Dephasing: $(\Phi_{p},\Phi_{p^{\prime}})$	$=1$	$>0$ if $(1-\varepsilon)p\leq p^{\prime}\leq(1+\varepsilon)p$
Amplitude damping: $(\mathcal{A}_{p_{1}},\mathcal{A}_{p_{2}})$	$\sqrt{\frac{1-p_{1}}{1-p_{2}}}$	$>0$ .