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Optimal conversion of nonlocal unitary operations

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http://pubman.mpdl.mpg.de/cone/persons/resource/persons60441

Cirac,  J. Ignacio
Theory, Max Planck Institute of Quantum Optics, Max Planck Society;

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Dür, W., Vidal, G., & Cirac, J. I. (2002). Optimal conversion of nonlocal unitary operations. Physical Review Letters, 89(5): 057901. 057901. Retrieved from http://link.aps.org/abstract/PRL/v89/e057901.


Cite as: http://hdl.handle.net/11858/00-001M-0000-000F-C1EB-3
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.