Physical realizations of quantum operations

Francesco Buscemi, G. Mauro D’Ariano, and Massimiliano F. Sacchi
Phys. Rev. A 68, 042113 – Published 23 October 2003
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Abstract

Quantum operations (QO’s) describe any state change allowed in quantum mechanics, such as the evolution of an open system or the state change due to a measurement. We address the problem of which unitary transformations and which observables can be used to achieve a QO with generally different input and output Hilbert spaces. We classify all unitary extensions of a QO and give explicit realizations in terms of free-evolution direct-sum dilations and interacting tensor-product dilations. In terms of Hilbert space dimensionality the free-evolution dilations minimize the physical resources needed to realize the QO, and for this case we provide bounds for the dimension of the ancilla space versus the rank of the QO. The interacting dilations on the other hand, correspond to the customary ancilla-system interaction realization, and for these we derive a majorization relation which selects the allowed unitary interactions between system and ancilla.

  • Received 29 May 2003

DOI:https://doi.org/10.1103/PhysRevA.68.042113

©2003 American Physical Society

Authors & Affiliations

Francesco Buscemi*, G. Mauro D’Ariano, and Massimiliano F. Sacchi‡,§

  • Quantum Optics & Information Group, INFM Unità di Pavia and Departimento di Fisica “A. Volta,” Università di Pavia, Via Bassi 6, I-27100 Pavia, Italy

  • *Electronic address: buscemi@fisicavolta.unipv.it
  • Also at Department of Electrical and Computer Engineering, Northwestern University, Evanston, IL 60208, USA. Electronic address: dariano@unipv.it
  • Electronic address: msacchi@unipv.it
  • §URL: http://www.qubit.it

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Issue

Vol. 68, Iss. 4 — October 2003

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