Minimal number of operators for observability of N-level quantum systems
type: Item
instance of: scholarly article
title: Minimal number of operators for observability of N-level quantum systems
zbMATH Open document ID: 0552.46043
DOI: 10.1007/BF02082903
published in: International Journal of Theoretical Physics
publication date: 1983-01-01T00:00:00Z
review text: 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.
reviewed by: Walter F. Wreszinski
Mathematics Subject Classification ID: 46N99
Mathematics Subject Classification ID: 81P10
zbMATH DE Number: 3879554
zbMATH Keywords: expectation values
zbMATH Keywords: statistical state
zbMATH Keywords: N-level quantum system
zbMATH Keywords: macroscopic information
zbMATH Keywords: von Neumann density matrix
author: Andrzej Jamiołkowski
MaRDI profile type: Publication
cites work: Q4169795
cites work: Q5551052
cites work: Information Theory and Statistical Mechanics
cites work: Q5638871
cites work: Infinite Systems of Classical Particles
cites work: Density Matrices Arising from Incomplete Measurements
cites work: Q3525854
description: scientific article; zbMATH DE number 3879554