Quantum Detection of Binary and Ternary Signals in the Presence of Thermal Noise Fields

A new technique for evaluating the performance of quantum signals observed in the presence of noise is described and evaluated. The quantum theory for detecting coherent-state signals has been developed previously; however, the quantum signal-plus-noise problem has received little attention due to its complexity. Here we develop a discrete approximation to the coherent-state representation of signal-plusnoise density operators, and present solutions to optimum receiver performance in terms of quantum measurement states whose performance is optimized via generalized rotations in Hilbert space. An efficient algorithm for carrying out the required numerical optimization is described and applied to binary signals observed in the presence of noise, for which exact results are available for comparison. The algorithm is then applied to the detection of ternary signals observed in the presence of noise, a previously unsolved problem, and the performance of the optimum receiver is characterized.