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On the efficiency of nonlocal gates generation

Berry Groisman·Benni Reznik
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Abstract

We propose and study a method for using non-maximally entangled states to implement probabilistically non-local gates. Unlike distillation-based protocols, this method does not generate a maximally entangled state at intermediate stages of the process. As a consequences, the method becomes more efficient at a certain range of parameters. Gates of the form $\exp[iξσ_{n_A}σ_{n_B}]$ with $ξ\ll1$, can be implemented with nearly unit probability and with vanishingly small entanglement, while for the distillation-based method the gate is produced with a vanishing success probability. We also derive an upper bound to the optimal success probability and show that in the small entanglement limit, the bound is tight.

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Berry Groisman, Benni Reznik. 2004-10-21. On the efficiency of nonlocal gates generation. https://doi.org/10.1103/physreva.71.032322

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