Entanglement Generation by Communication using Phase-Squeezed Light with Photon Loss

In order to implement fault-tolerant quantum computation, entanglement generation with low error probability and high success probability is required. We have proposed the use of squeezed coherent light as a probe to generate entanglement between two atoms by communication, and shown that the error probability is reduced well below the threshold of fault-tolerant quantum computation [Phys. Rev. A. {\bf 88}, 022313 (2013)]. Here, we investigate the effect of photon loss mainly due to finite coupling efficiency to the cavity. The error probability with the photon loss is calculated by the beam-splitter model for homodyne measurement on probe light. Optimum condition on the amplitude of probe light to minimize the error probability is examined. It is shown that the phase-squeezed probe light yields lower error probability than coherent-light probe. A fault-tolerant quantum computation algorithm can be implemented under 0.59 dB loss by concatenating five-qubit error correction code.