CONDITIONAL PROBABILITIES FOR A SINGLE-PHOTON AT A BEAM SPLITTER

Eight-port homodyne detection may be used to perform a joint measureme nt on a single-mode input to a beam splitter; the x quadrature is meas ured at one output port, and the p quadrature is measured at the other . This is possible even when the input mode contains only one photon. We show to what extent this ''joint measurement of a single photon'' m ay be reconciled with the semiclassical notion that the photon may onl y exit from one of the beam splitter output ports.