Optimal Conversion of Nonlocal Unitary Operations

W. Dür, G. Vidal, and J.  I. Cirac
Phys. Rev. Lett. 89, 057901 – Published 15 July 2002

Abstract

We study when a nonlocal unitary operation acting on two d-level systems can probabilistically simulate another one when arbitrary local operations and classical communication are allowed. We provide necessary and sufficient conditions for the simulation to be possible. Probabilistic interconvertability is used to define an equivalence relation between gates. We show that this relation induces a finite number of classes that we identify. In the case of two qubits, two classes of nonlocal operations exist. We show how the representatives of these classes, CNOT and SWAP, can be deterministically converted into any operation of its class and calculate the optimal probability of the reverse process.

  • Received 20 December 2001

DOI:https://doi.org/10.1103/PhysRevLett.89.057901

©2002 American Physical Society

Authors & Affiliations

W. Dür1, G. Vidal2, and J.  I. Cirac3

  • 1Sektion Physik, Ludwig-Maximilians-Universität München, Theresienstrasse 37, D-80333 München, Germany
  • 2Institut für Theoretische Physik, Universität Innsbruck, A-6020 Innsbruck, Austria
  • 3Max-Planck Institut für Quantenoptik, Hans-Kopfermann Strasse 1, D-85748 Garching, Germany

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Issue

Vol. 89, Iss. 5 — 29 July 2002

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