State-independent violation of correlation inequalities for non-contextual theories

Xinyu Pan, Yanchun Chang, Gang‐Qin Liu +1 more

Quantum mechanics implies that not all physical properties can be simultaneously well defined, such as the momentum and position due to Heisenberg uncertainty principle. Some alternative theories have been explored, notably the non-contextual hidden variable theories in which the properties of a system have pre-defined values which are independent of the measurement contextual. However, the Kochen-Specker theorem showed that such non-contextual hidden variable theories are in conflict with quantum mechanics. Recently, a state-independent inequality satisfied by non-contextual hidden variable theories and violated by quantum mechanics is proposed in the simplest three-state system (a qutrit) by the least 13 projection measurement rays. Here, we report an experimental demonstration of the violation of this inequality. This provides a state-independent experimental test of quantum contextuality, for the first time in solid state system, by a natural qutrit of nitrogen-vacancy center in diamond at room temperature.

Devashish Pandey, Xavier Oriols, Guillermo Albareda

Adán Cabello

We show that there are Bell-type inequalities for noncontextual theories that are violated by any quantum state. One of these inequalities between the correlations of compatible measurements is particularly suitable for testing this state-independent violation in an experiment.

Yoshihiro Maruyama

Arthur I. Fine

Adán Cabello

There are experimentally testable correlation Bell inequalities which are satisfied by any noncontextual theory but are violated by any quantum state. We discuss how to test one of them.