acta physica slovaca

Acta Physica Slovaca 61, No.3, 273-390 (2011) (118 pages)


A. Bisio1, G. Chiribella2, G. M. D'Ariano1, P. Perinotti1
    1 Quit group, Dipartimento di Fisica A. Volta, via Bassi 6, 27100 Pavia, Italy
    2 Perimeter Institute for Theoretical Physics, 31 Caroline St. North, Waterloo, Ontario N2L 2Y5, Canada

Full text: ::pdf :: (Received 29 August 2011, accepted 30 August 2011)

Abstract: In this work we present a general mathematical framework to deal with Quantum Networks, i.e. networks resulting from the interconnection of elementary quantum circuits. The cornerstone of our approach is a generalization of the Choi isomorphism that allows one to efficiently represent any given Quantum Network in terms of a single positive operator. Our formalism allows one to face and solve many quantum information processing problems that would be hardly manageable otherwise, the most relevant of which are reviewed in this work: quantum process tomography, quantum cloning and learning of transformations, inversion of a unitary gate, information-disturbance tradeoff in estimating a unitary transformation, cloning and learning of a measurement device.

DOI: 10.2478/v10155-011-0003-9
PACS: 03.65.-w, 03.65.Fd, 03.67.Ac
Keywords: Quantum Information Processing, Quantum Circuits, Quantum Networks, Quantum Tomography, Quantum Cloning, Quantum Learning, Unitary Channels, Group theory in Quantum Mechanics
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