Robert B. Griffiths
Carnegie-Mellon University, USA
Quantum measurements and contextuality
Quantum contextuality has to do with measurements of a collection of quantum observables, not all of which commute with each other, and hence cannot all be measured simultaneously. Bell [Rev. Mod. Phys. 38 (1966) 447] posed the following question: If A commutes with B and also with C, but B and C do not commute, will the value of A measured along with B differ from its value if measured along with C? If “yes”, quantum mechanics is contextual in that the measured value of A depends on the context, {A,B} or {A,C}; if “no”, quantum mechanics is noncontextual. Using an analysis of quantum measurements not available to Bell I will argue that quantum mechanics is noncontextual. To be precise, if a measurement of A with B yields a value A=a, then had the same experiment been carried out with apparatus modified to measure A along with C, the same value A=a would have been obtained. More recent literature employs “contextual” with a different meaning from that used by Bell. Thus in a proposal by Abramsky et al. [Phys. Rev. Lett. 119 (2017) 050504] noncontextuality is associated with the existence of a joint probability distribution for outcomes of measurements of a collection of observables, not all of which commute. While this definition poses some interesting mathematical problems, I will argue that it is not related in any simple way to the physics of quantum measurements.
