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Phys. Rev. A 70, 012315 (2004) [7 pages]

Purity and state fidelity of quantum channels

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Paolo Zanardi
Institute for Scientific Interchange (ISI), Villa Gualino, Viale Settimio Severo 65, I-10133 Torino, Italy, and Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

Daniel A. Lidar
Chemical Physics Theory Group, Chemistry Department, and Center for Quantum Information and Quantum Control, University of Toronto, 80 Saint George Street, Toronto, Ontario M5S 3H6, Canada

Received 9 March 2004; published 29 July 2004

We associate with every quantum channel T acting on a Hilbert space H a pair of Hermitian operators, referred to as “Hamiltonians,” over the symmetric subspace of H⊗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.

© 2004 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevA.70.012315
DOI:
10.1103/PhysRevA.70.012315
PACS:
03.67.Hk
 
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