Optimization of Quantum Universal Detectors

The expectation value ?O? of an arbitrary operator O can be obtained via a uni- versal measuring apparatus that is independent of O, by changing only the data- processing of the outcomes. Such a "universal detector" performs a joint mea- surement on the system and on a suitable ancilla prepared in a fixed state, and is equivalent to a positive operator valued measure (POVM) for the system that is "informationally complete". The data processing functions generally are not unique, and we pose the problem of their optimization, providing some examples for covariant POVM's, in particular for SU(d) covariance group.