Probabilistic quantum multimeters

We propose quantum devices that can realize probabilistically different projective measurements on a qubit. The desired measurement basis is selected by the quantum state of a program register. First we analyze the phase-covariant multimeters for a large class of program states, then the universal multimeters for a special choice of program. In both cases we start with deterministic but erroneous devices and then proceed to devices that never make a mistake but from time to time they give an inconclusive result. These multimeters are optimized (for a given type of a program) with respect to the minimum probability of inconclusive result. This concept is further generalized to the multimeters that minimize the error rate for a given probability of an inconclusive result (or vice versa). Finally, we propose a generalization for qudits.