Abstract:The goal is to extend Gleason's notion of a frame function, which is essential in his fundamental theorem in quantum measurement, to a more general function acting on 1-tight, socalled, Parseval frames. We refer to these functions as Gleason functions for Parseval frames. The reason for our generalization is that positive operator valued measures (POVMs) are essentially equivalent to Parseval frames, and that POVMs arise naturally in quantum measurement theory. We prove that under the proper assumptions, Gleas… Show more
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