Optimal Bounds on Functions of Quantum States under Quantum Channels

Let $ρ_1, ρ_2$ be quantum states and $(ρ_1,ρ_2) \mapsto D(ρ_1, ρ_2)$ be a scalar function such as the trace norm, the fidelity, and the relative entropy, etc. We determine optimal bounds for $D(ρ_1, Φ(ρ_2))$ for $Φ\in \mathcal{S}$ 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.

No reviews yet.

No comments yet.