Entropic measurement uncertainty relations for spin observables
Year: 2019
Type: article
Abstract: The information-theoretic formulation of quantum measurement uncertainty \nrelations (MURs), based on the notion of relative entropy between measurement \nprobabilities, is extended to the set of all the spin components for a generic \nspin $s$. For a physical class of approximate joint measurements of the spin \ncomponents, we define the device information loss as the maximum loss of \ninformation per observable occurring in approximating the ideal incompatible \ncomponents with the joint measurement at hand. By optimizing on the measuring \ndevice, we define the notion of minimum information loss. By using this \nnotions, we show how to give a significant formulation of state independent \nMURs in the case of infinitely many target observables. The same construction \nworks as well for finitely many observables, and we study the related MURs for \ntwo and three orthogonal spin components. The minimum information loss plays \nalso the role of measure of incompatibility and in this respect it allows us to \ncompare quantitatively the incompatibility of various sets of spin observables, \nwith different number of involved components and different values of $s$.
Authors: Alberto Barchielli, Matteo Gregoratti
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2995668644