Optimal measurements in quantum mechanics

Abstract

Four common optimality criteria for measurements are formulated using relations in the set of observables, and their connections are clarified. As case studies, 1-0 observables, localization observables, and photon counting observables are considered.Comment: minor correction

Quantal effects and MaxEnt

“…The specifical form of an effect in quantum mechanics is as follows. A generalized observable or positive operator valued measure (POVM) [23][24][25] will be represented by a mapping E : B(R) → B(H) such that…”

State Determination and Sufficiency of Observables

“…Let us first recall, following [2] Definition States ρ and ϕ are distinguished by semispectral measure e if…”

“…Proof On account of [1,2] for spectral measure E, set D E consists only of vector states ϕ such that their density matrices are one-dimensional projections from the range of E. So…”

“…In the first part we have investigated state determination power of a semispectral measure and its correlation with sufficiency but it is also possible to consider distinction power. Following [2] The problem of relationship between algebra generated by a spectral measure e and family of states that is determined by e remains unresolved, as well as a structure of D e for any measurement e is open issue.…”

“…State determination and distinction was investigated in [2] and [1]. Two questions are dealt with in this paper: when the W * -algebra generated by spectral or semispectral measure e is sufficient for a family of states D e (the set of states determined by e) and what is the characterization of more general set D N of all states determined by W * -algebra N .…”