  We investigate quantum measurement strategies capable of discriminating two
coherent states probabilistically with significantly smaller error
probabilities than can be obtained using non- probabilistic state
discrimination. We apply a postselection strategy to the measurement data of a
homodyne detector as well as a photon number resolving detector in order to
lower the error probability. We compare the two different receivers with an
optimal intermediate measurement scheme where the error rate is minimized for a
fixed rate of inconclusive results. The photon number resolving (PNR) receiver
is experimentally demonstrated and compared to an experimental realization of a
homodyne receiver with postselection. In the comparison it becomes clear, that
the perfromance of the new PNR receiver surpasses the performance of the
homodyne receiver, which we proof to be optimal within any Gaussian operations
and conditional dynamics.
