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A concrete procedure for obtaining sharp reconstructions of unsharp observables in finite-dimensional quantum mechanics |
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| Authors: | Gianpiero Cattaneo Tiziana Marsico Giuseppe Nisticò Guido Bacciagaluppi |
| Institution: | (1) Dipartimento di Scienze dell'Informazione, Università di Milano, Milan, Italy;(2) Dipartimento di Matematica, Università di Milano, Milan, Italy;(3) Dipartimento di Matematica, Università della Calabria, Arcavacata, Italy;(4) Balliol College, Oxford, UK;(5) Sub-Faculty of Philosophy, University of Oxford, UK |
| Abstract: | We discuss the problem of how a (commutative) generalized observable in a finite-dimensional Hilbert space (communtative effect-valued resolution of the identity) can be considered as an unsharp realization of some standard observable (projection-valued resolution of the identity). In particular, we give a concrete procedure for constructing such a standard observable. Some results about the “uniqueness” of the resulting observable are also examined. |
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