On constructing informationally complete covariant positive operator-valued measures

• URL: http://arxiv.org/abs/2301.12492v1
• Date: Sun, 29 Jan 2023 16:57:56 GMT
• Title: On constructing informationally complete covariant positive operator-valued measures
• Authors: Grigori Amosov
• Abstract summary: 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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