Probabilistic implementation of a nonlocal operation using a nonmaximally entangled state
Lin Chen, Yi-Xin Chen · Physical Review A · 2005
We develop the probabilistic implementation of a nonlocal gate $\mathrm{exp}[i\ensuremath{\xi}{\ensuremath{\sigma}}_{{n}_{A}}{\ensuremath{\sigma}}_{{n}_{B}}]$ and $\ensuremath{\xi}∊[0,(\ensuremath{\pi}∕4)]$, by using a single nonmaximally entangled state. We prove that nonlocal gates can be implemented with a fidelity of $>79.3%$ and a consumption of $<0.969\phantom{\rule{0.3em}{0ex}}\mathrm{ebits}$ and two classical bits, when $\ensuremath{\xi}\ensuremath{\leqslant}0.353$. This provides a higher bound for the feasible operation compared to the former techniques. Besides, gates with $\ensuremath{\xi}\ensuremath{\geqslant}0.353$ can be implemented with the probability 79.3% and a consumption of 0.969 ebits, which is the same efficiency as the distillation-based protocol, while our method saves extra classical resources. Gates with $\ensuremath{\xi}\ensuremath{\rightarrow}0$ can be implemented with nearly unit probability and a small entanglement. We also generalize some applications to the multiple system, where we find it is possible to implement certain nonlocal gates between many nonentangled partners using a nonmaximally multiple entangled state.