Geometry of quantum signal detection.

Consideration of a binary quantum signal detection problem in a two-dimensional Hilbert space. The optimum detection problem is reduced to the problem of finding the locus of a vector which has a maximum projection along the fixed a priori probability vector of hypotheses. It is shown that the desired locus can be determined by a geometrical method involving the use of a randomized decision strategy. It is further shown that this geometrical method can be applied to the optimum solution of a binary detection problem described in a product Hilbert space.