On constructing informationally complete covariant positive operator-valued measures

Grigori Amosov

doi:10.3390/e25050783

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arXiv · 2301.12492

On constructing informationally complete covariant positive operator-valued measures

Grigori Amosov

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Abstract

We study positive operator-valued measures generated by orbits of projective unitary representations of locally compact Abelian groups. It is shown that integration over such a measure defines a family of contractions being multiples of unitary operators from the representation. Using this fact it is proved that the measures are informationally complete. The obtained results are illustrated for the measure with density taking values in the set of coherent states.

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Grigori Amosov. 2023-01-29. On constructing informationally complete covariant positive operator-valued measures. https://doi.org/10.3390/e25050783

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