Reviews in Mathematical Physics

PROBABILITY STRUCTURES FOR QUANTUM STATE SPACES

Paul Busch, Gianni Cassinelli, PEKKA J. LAHTI

Published Oct 1, 1995• 22 citations

Abstract

The theme of this paper is to represent the states of a quantum system by means of probability measures. We fix a positive operator valued measure E on a measurable space (Ω, ℬ(Ω)) acting in a Hilbert space ℋ, and we study the properties of the mapping that it induces from the set of trace class operators on ℋ to the set of measures on (Ω, ℬ(Ω)). In particular, the injectivity and the surjectivity of this map are characterised in terms of the properties of E.

DOI: 10.1142/s0129055x95000402

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