Equivalence classes of non-local unitary operations

Dür, W.; Cirac, J. Ignacio

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Equivalence classes of non-local unitary operations

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

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Dür, W., & Cirac, J. I. (2002). Equivalence classes of non-local unitary operations. Quantum Information & Computation, 2(3), 240-254. Retrieved from http://www.rintonpress.com/journals/qic-2-3/240-254.pdf.

Cite as: https://hdl.handle.net/11858/00-001M-0000-000F-C223-E

Abstract

We study when a multipartite non-local unitary operation can deterministically or probabilistically simulate another one when local operations of a certain kind-in some cases including also classical communication-are allowed. In the case of probabilistic simulation and allowing for arbitrary local operations, we provide necessary and sufficient conditions for the simulation to be possible. Deterministic and probabilistic interconversion under certain kinds of local operations are used to define equivalence relations between gates. In the probabilistic, bipartite case this induces a finite number of classes. In multiqubit systems, however, two unitary operations typically cannot simulate each other with non-zero probability of success. We also show which kind of entanglement can be created by a given non-local unitary operation and generalize our results to arbitrary operators.