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Purity and State Fidelity of Quantum Channels via Hamiltonians

Paolo Zanardi·Daniel Lidar
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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.

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Paolo Zanardi, Daniel Lidar. 2004-03-09. Purity and State Fidelity of Quantum Channels via Hamiltonians. https://doi.org/10.1103/physreva.70.012315

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