Implementing nonlocal gates with nonmaximally entangled states
Berry Groisman, Benni Reznik · Physical Review A · 2005
We propose and study a method for using nonmaximally entangled states to probabilistically implement desired nonlocal gates. Unlike distillation-based protocols, this method does not generate a maximally entangled state at intermediate stages of the process. As a consequence, the method becomes more efficient at a certain range of parameters. Gates of the form $\mathrm{exp}[i\ensuremath{\xi}{\ensuremath{\sigma}}_{{n}_{A}}{\ensuremath{\sigma}}_{{n}_{B}}]$ with $\ensuremath{\xi}⪡1$ 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.