Detection of Quantum Signals by a Mismatched Receiver
Carl W. Helstrom · Journal of Information and Optimization Sciences · 1980
A quantum receiver is modelled as a harmonic oscillator imperfectly matched to the incident signal-bearing field. At the beginning of its interaction with the field the oscillator is primed by being placed in a predetermined quantum state. It is shown how to calculate the state of this oscillator at the end of the observation interval both in the presence and in the absence of an incident coherent signal. As examples the error probabilities of a binary on-off communication system with such a mismatched receiver are calculated (a) for a signal of known phase, the receiver primed with a two-photon coherent state, and (b) for a signal of random phase, the receiver primed with a number eigenstate. In both cases the error probability depends on the mean number of externally available signal photons when the number of photons in the priming state is very large, rather than on the smaller number that would actually be absorbed by the mismatched receiver unprimed.