More on a trace inequality in quantum information theory

Abstract

It is known that for a completely positive and trace preserving (cptp) map $\mathcal{N}$, $\text{Tr}$ $\exp$$\{\log \sigma$ $+$ ${\mathcal{N}}^{†}[\log \mathcal{N}(\rho )$ $-\log \mathcal{N}(\sigma )]\}$ $⩽$ $\text{Tr}$ $\rho$ when $\rho$, $\sigma$, $\mathcal{N}(\rho )$, and $\mathcal{N}(\sigma )$ are strictly positive. We state and prove a relevant version of this inequality for the hitherto unaddressed case of these matrices being nonnegative. Our treatment also provides an alternate proof for the strictly positive case.

9 pages

References in corpus (4)

• On quantum Renyi entropies: a new generalization and some properties
• Strong converse for the classical capacity of entanglement-breaking and Hadamard channels via a sandwiched Renyi relative entropy
• Strengthened Monotonicity of Relative Entropy via Pinched Petz Recovery Map
• Remainder Terms for Some Quantum Entropy Inequalities