Purity and State Fidelity of Quantum Channels via Hamiltonians

Abstract

We associate to every quantum channel $T$ acting on a Hilbert space $\mathcal{H}$ a pair of Hamiltonian operators over the symmetric subspace of ${\mathcal{H}}^{\otimes 2}$. The expectation values of these Hamiltonians over symmetric product states give either the purity or the pure state fidelity of $T$. This allows us to analytically compute these measures for a wide class of channels, and to identify states that are optimal with respect to these measures.

7 Pages

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