paper

Quantum realization of arbitrary joint measurability structures

arXiv:1311.5948 · doi:10.1103/PhysRevA.89.052126

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.

6 pages, 3 figures; minor additions to the text; this is close to the published version; title changed on publication when someone at Phys. Rev. A. insisted: "we strongly prefer to avoid titles in the form of full sentences (containing both a subject and a verb) because titles should indicate what is being studied, rather than consist of a narrowly focused statement."

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