Quantum realization of arbitrary joint measurability structures

Ravi Kunjwal, Chris Heunen, Tobias Fritz

Research output: Contribution to journalArticlepeer-review

Abstract

In many a traditional physics textbook, a quantum measurement is defined as a projective measurement represented by a Hermitian operator. In quantum information theory, however, the concept of a measurement is dealt with in complete generality and we are therefore forced to confront the more general notion of positive-operator valued measures (POVMs), which suffice to describe all measurements that can be implemented in quantum experiments. We study the (in)compatibility of such POVMs and show that quantum theory realizes all possible (in)compatibility relations among sets of POVMs. This is in contrast to the restricted case of projective measurements for which commutativity is essentially equivalent to compatibility. Our result therefore points out a fundamental feature with respect to the (in)compatibility of quantum observables that has no analog in the case of projective measurements.
Original languageEnglish
Article number052126
Number of pages5
JournalPhysical Review A
Volume89
Issue number5
DOIs
Publication statusPublished - 21 May 2014

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