Complete measurements of quantum observables
Juha-Pekka Pellonp\"a\"a
TL;DR
This paper introduces the concept of complete measurements in quantum mechanics, which fully refine POVMs to extract maximal information, and demonstrates how any POVM can be measured completely with minimal ancillary systems.
Contribution
It formalizes complete measurements of POVMs, shows their universality via sequential measurements, and optimizes the ancillary space needed.
Findings
Complete measurements provide detailed outcome multiplicities.
Any POVM can be measured completely through sequential procedures.
Minimal ancillary spaces are sufficient for complete measurements.
Abstract
We define a complete measurement of a quantum observable (POVM) as a measurement of the maximally refined version of the POVM. Complete measurements give information from 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.
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