  We propose quantum receivers with optical squeezing and
photon-number-resolving detector (PNRD) for the near-optimal discrimination of
quaternary phase-shift-keyed coherent state signals. The basic scheme is
similar to the previous proposals (e.g. Phys. Rev. A 84, 042328 (2012)) in
which displacement operations, on-off detectors, and electrical feedforward
operations were used. Here we study two types of receivers where one installs
optical squeezings and the other uses PNRDs instead of on-off detectors. We
show that both receivers can attain lower error rates than that by the previous
scheme and in particular, the PNRD based receiver has a significant gain under
the fixed number of feedfoward steps. Moreover, we show that the PNRD based
receiver can suppress the errors due to dark counts, which is not possible by
the on-off detector based receiver with a limited number of feedforwards.
