Measurements Incompatible in Quantum Theory Cannot Be Measured Jointly in Any Other No-Signaling Theory
Year: 2009
Type: article
Abstract: It is well known that jointly measurable observables cannot lead to a violation of any Bell inequality--independent of the state and the measurements chosen at the other site. In this Letter we prove the converse: every pair of incompatible quantum observables enables the violation of a Bell inequality and therefore must remain incompatible within any other no-signaling theory. While in the case of von Neumann measurements it is sufficient to use the same pair of observables at both sites, general measurements can require different choices. The main result is obtained by showing that for arbitrary dimension the Clauser-Horne-Shimony-Holt inequality provides the Lagrangian dual of the characterization of joint measurability. This leads to a simple criterion for joint measurability beyond the known qubit case.
Source: Physical Review Letters
Institutions: University of Copenhagen, Universidad Complutense de Madrid
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1992082016