A note on the Relationship between Localization and Norm-1 Property
Quantum Physics
2015-06-12 v1 Mathematical Physics
math.MP
Abstract
The paper focuses on the problem of localization in quantum mechanics. It is well known that it is not possible to define a localization observable for the photon by means of projection valued measures. Conversely, that is possible by using positive operator valued measures. On the other hand, projection valued measures imply a kind of localization which is stronger than the one implied by positive operator valued measures. It has been claimed that the norm-1 property would in some sense reduce the gap between the two kind of localizations. We give a necessary condition for the norm-1 property and show that it is not satisfied by several important localization observables.
Cite
@article{arxiv.1211.3847,
title = {A note on the Relationship between Localization and Norm-1 Property},
author = {Roberto Beneduci and Franklin E. Schroeck},
journal= {arXiv preprint arXiv:1211.3847},
year = {2015}
}