Statistical signal detection is formulated quantum-mechanically in terms of choosing one of two density operators as the better description of the state of an ideal receiver after exposure to a field in which a signal may or may not be present. The optimum decision procedure is expressed as a projection operator on the state-space of the receiver. Examples involving the single-mode detection of coherent and incoherent signals are given. Threshold detection as an approximation to optimum detection for weak signals is also defined quantum-mechanically, and threshold detectors for coherent and incoherent fields occupying many modes of a receiver cavity are worked out. The noise in all cases is taken to be thermal radiation described by the Planck law. © 1967 Academic Press Inc.
Helstrom, C. W. (1967). Detection theory and quantum mechanics. Information and Control, 10(3), 254–291. https://doi.org/10.1016/S0019-9958(67)90302-6