Optimal Bounds on Functions of Quantum States under Quantum Channels

Abstract

Let ${\rho }_1,{\rho }_2$ be quantum states and $({\rho }_1,{\rho }_2)\mapsto D({\rho }_1,{\rho }_2)$ be a scalar function such as the trace norm, the fidelity, and the relative entropy, etc. We determine optimal bounds for $D({\rho }_1,\Phi ({\rho }_2))$ for $\Phi \in \mathcal{S}$ for different class of functions $D(\cdot ,\cdot )$, where $\mathcal{S}$ is the set of unitary quantum channels, the set of mixed unitary channels, the set of unital quantum channels, and the set of all quantum channels.

References in corpus (1)

• Quantum fidelity and relative entropy between unitary orbits