INFORMATIONALLY COMPLETE JOINT MEASUREMENTS ON FINITE QUANTUM SYSTEMS

Abstract. We show that there are informationally complete joint measurements of two conjugated observables on a finite quantum system, meaning that they enable to identify all quantum states from their measurement outcome statistics. We further demon-strate that it is possible to implement a joint observable as a se-quential measurement. If we require minimal noise in the joint measurement, then the joint observable is unique. If the dimension d is odd, then this observable is informationally complete. But if d is even, then the joint observable is not informationally complete and one has to allow more noise in order to obtain informational completeness. 1