Minimal number of operators for observability of N-level quantum systems
The paper discusses the minimal number \(n_{\min}\) of operators \(A_ 1,...,A_ n\), whose expectation values at certain instants determine the statistical state of an N-level quantum system (a system described on an N-dimensional Hilbert space). It is assumed that the macroscopic information about the system is given by the mean values \(tr[\rho (t_ j)A_ i]=m_ i(t_ j)\) of n self-adjoint operators \(A_ 1,...,A_ n\) at instants of time \(t_ 1<t_ 2<...<t_ s\), where \(s<N^ 2-1\), and \(\rho\) is the von Neumann density matrix, which satisfies the equation \(i{\dot \rho}(t)=[H,\rho (t)]\) with H the system's Hamiltonian. The mathematical framework is elementary linear algebra.
scientific article; zbMATH DE number 3879554