Minimal number of operators for observability ofN-level quantum systems

Abstract

This paper discusses the minimal numbernmin of operatorsA1,...,A n , whose expectation values at some instants determine the statistical state of anN-level quantum system. We assume that the macroscopic information about the system in question is given by the mean values Tr[ρ(t j )A i ]=m i (t j ) ofn self-adjoint operatorsA1,...,A n at some instantst1<t2<⋯<t s , wheres<N2−1.