Notes on coarse grainings and functions of observables

Anatolij Dvurečenskij, Pekka Lahti, Sylvia Pulmannová, Kari Ylinen
2005 Reports on mathematical physics  
Using the Naimark dilation theory we investigate the question under what conditions an observable which is a coarse graining of another observable is a function of it. To this end, conditions for the separability and for the Boolean structure of an observable are given.
doi:10.1016/s0034-4877(05)80030-8 fatcat:io65xzigjncn3lfewauobb4che