Probabilistically implementing nonlocal operation using non-maximally entangled state

Abstract

We develop the probabilistic implementation of a nonlocal gate $\exp [i\xi {\sigma }_{n_A}{\sigma }_{n_B}]$ and $\xi \in [0,\frac{\pi }{4}]$, by using a single non-maximally entangled state. We prove that, nonlocal gates can be implemented with a fidelity greater than 79.3% and a consumption of less than 0.969 ebits and 2 classical bits, when $\xi \le 0.353$. This provides a higher bound for the feasible operation compared to the former techniques \cite{Cirac,Groisman,Bennett-1}. Besides, gates with $\xi \ge 0.353$ 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 \cite{Groisman,Bennett-1}, while our method saves extra classical resource. Gates with $\xi \to 0$ can be implemented with nearly unit probability and a small entanglement. We also generalize some application to the multiple system, where we find it is possible to implement certain nonlocal gates between many non-entangled partners using a non-maximally multiple entangled state.

5 pages,1 figure

References in corpus (5)

• Information and Computation: Classical and Quantum Aspects
• Experimental Teleportation of a Quantum Controlled-NOT Gate
• Optimal conversion of non--local unitary operations
• Remote operations and interactions for systems of arbitrary dimensional Hilbert space: a state-operator approach
• Non-local Operations: Purification, storage, compression, tomography, and probabilistic implementation

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