Notes on coarse grainings and functions of observables
arXiv:quant-ph/0411136 · doi:10.1016/S0034-4877(05)80030-8
Abstract
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.