Abstract
We derive an exact expression for the joint count probability in an eight-port homodyne detector, when the signal field is in an arbitrary state, the local oscillator is in a coherent state and the other two input states are the vacuum. In the limit of a strong local oscillator this photon count statistics is the scaled Q-function of the signal state. The phase distribution corresponding to this measurement scheme is then the Q-function of the signal field integrated over radius. The physical reason for the Q-function lies in the simultaneous measurement of two two-mode operators. We discuss the dependence of the photon count statistics on the local oscillator intensity using the example of a one-photon Fock state.
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