Covariant quantum measurements may not be optimal

Abstract

Quantum particles, such as spins, can be used for communicating spatial\ndirections to observers who share no common coordinate frame. We show that if\nthe emitter's signals are the orbit of a group, then the optimal detection\nmethod may not be a covariant measurement (contrary to widespread belief). It\nmay be advantageous for the receiver to use a different group and an indirect\nestimation method: first, an ordinary measurement supplies redundant numerical\nparameters; the latter are then used for a nonlinear optimal identification of\nthe signal.\n