Complete Measurements of Quantum Observables
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We define a complete measurement of a quantum observable (POVM) as a measurement of the maximally refined (rank-1) version of the POVM. Complete measurements give information on the multiplicities of the measurement outcomes and can be viewed as state preparation procedures. We show that any POVM can be measured completely by using sequential measurements or maximally refinable instruments. Moreover, the ancillary space of a complete measurement can be chosen to be minimal.
KeywordsQuantum observable Positive operator valued measure Instrument Measurement model Rank-1 observable Maximally refined observable Sequential measurement
This work was supported by the Academy of Finland grant No. 138135.
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