  We address the limit of the Gaussian operations and classical communication
in the problem of quantum state discrimination. We show that the optimal
Gaussian strategy for the discrimination of the binary phase shift keyed (BPSK)
coherent signal is a simple homodyne detection. We also propose practical
near-optimal quantum receivers that beat the BPSK homodyne limit in all areas
of the signal power. Our scheme is simple and does not require realtime
electrical feedback.
