Quantum theory of the homodyne-direct receiver

A quantum-communication-theoretical approach to the homodyne-direct receiver is presented and used to obtain the quantum detection operators and average probability of error for any binary quantum-state signal. The effect of the quantum efficiency η of a photodetector used in the receiver is taken into account. Which quantum states have been received is determined by comparing the read-out of the receiver with a certain decision level; so the dependences of the detection operators and average probability of error on a decision level are also considered. As a quantum-state signal, the binary phaseshift keyed signal including thermal noise is investigated in detail, and the condition necessary for the average probability of error of the homodyne-direct receiver to be smaller than the standard quantum limit (the short noise limit) of the signal detection is obtained.