06/06/16 15:30H Talk @ UFRJ – Adrien Laversanne Finot – Univ. Paris Diderot, FrancePosted: May 25, 2016
General conditions for maximal violation of the Peres-Mermin inequality in discrete and continuous variables
In classical mechanics systems have intrinsic properties that are later revealed by the measurements. In particular the result of one measurement does not depend on previously made measurements. We say that classical mechanics is non-contextual. It is possible to demonstrate the contextual nature of quantum mechanics by the violation of inequalities based on correlation measurements of well chosen observables. Surprisingly it is possible to find inequalities that are violated by any state . These inequalities have been designed separately for both discrete and continuous variable measurements . In this talk I show how to test contextuality in the Peres-Mermin scenario with measurements of observables acting on Hilbert spaces of arbitrary dimension. By unifying this two strategies we are able to derive general conditions to have a state independent maximal violation of the inequality . This condition allow us to characterize the spectral decomposition of observables that are suitable for maximal state independent violation of the non-contextual bound. This characterization makes a formal connection between different observables that were previously derived independently. As a consequence of this result, we find that it is impossible to obtain a maximal state-independent violation of non-contextuality with discrete observables of odd dimensions.
 A. Cabello, Phys. Rev. Lett. 101, 210401 (2008).
 A. Asadian, C. Budroni, F. E. S. Steinhoff, P. Rabl, and O. Gühne, Phys. Rev. Lett. 114, 250403 (2015).
 A. Laversanne-Finot, A. Ketterer, M. R. Barros, S. P. Walborn, T. Coudreau, A. Keller, P. Milman, arXiv:1512.03334, (2015).
UFRJ- Centro de Tecnologia do Fundão, Bloco A, sala 343