Positive operator-valued measures and densely-defined operator-valued frames
Functional Analysis
2020-04-27 v1
Abstract
In the signal-processing literature, a frame is a mechanism for performing analysis and reconstruction in a Hilbert space. By contrast, in quantum theory, a positive operator-valued measure (POVM) decomposes a Hilbert-space vector for the purpose of computing measurement probabilities. Frames and their most common generalizations can be seen to give rise to POVMs, but does every reasonable POVM arise from a type of frame? In this paper we answer this question using a Radon-Nikodym-type result.
Keywords
Cite
@article{arxiv.2004.11729,
title = {Positive operator-valued measures and densely-defined operator-valued frames},
author = {Benjamin Robinson and Bill Moran and Doug Cochran},
journal= {arXiv preprint arXiv:2004.11729},
year = {2020}
}
Comments
9 pages, submitted to the Rocky Mountain Math Journal