Continuous-variable controlled-Z gate using an atomic ensemble

The continuous-variable controlled-Z gate is a canonical two-mode gate for universal continuous-variable quantum computation. It is considered as one of the most fundamental continuous-variable quantum gates. Here we present a scheme for realizing continuous-variable controlled-Z gate between two optical beams using an atomic ensemble. The gate is performed by simply sending the two beams propagating in two orthogonal directions twice through a spin-squeezed atomic medium. Its fidelity can run up to one if the input atomic state is infinitely squeezed. Considering the noise effects due to atomic decoherence and light losses, we show that the observed fidelities of the scheme are still quite high within presently available techniques.