Equivalence classes of non-local unitary operations

Details Equivalence classes of non-local unitary operations Equivalence classes of non-local unitary operations

2002-01-25

arxiv.org/abs/quant-ph/0201112v2

Quantum Information and Computation, Vol. 2, No. 3, 240-254 (2002)

Physics

Quantum Physics

(1) 9 pages, no figures, submitted to QIC; (2) reference added, minor changes

Scientific paper

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.

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