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On probabilistic operator-valued measures based on frames G. G. Amosov |
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Abstract: In functional analysis, the frame theory is well known, which makes it possible to decompose the elements of a Hilbert space into sums of, generally speaking, linearly dependent vectors. Another task is to measure quantum states (positive operators with a unit trace), followed by their (possibly not exact) reconstruction. Our goal will be to apply frame theory to construct probabilistic operator-valued measures (that is, measures normalized to the identical operator). |
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