Density Matrices Arising from Incomplete Measurements

Abstract

The problem of how to associate a statistical ensemble of a quantum mechanical system with an incomplete set of measured ensemble averages is discussed. The view adhered to in this note is that the most chaotic ensemble consistent with the measured ensemble averages is a reasonable choice of ensemble. The properties of this ensemble are studied rigorously for the case when the quantum mechanical system is associated with a finite‐dimensional Hilbert space. The results are extended heuristically to some particular ensembles of many‐boson and many‐fermion systems.