1206.3212 (Mateus Araújo et al.)

Complete characterization of the n-cycle noncontextual polytope    [PDF]

Mateus Araújo, Marco Túlio Quintino, Costantino Budroni, Marcelo Terra Cunha, Adán Cabello

We show the minimal set of inequalities which completely separates quantum and noncontextual correlations for n dichotomic observables Xi, i = 0, ..., n - 1, such that Xi and Xi+1 (with the addition modulo n) are jointly measurable. This generalizes to arbitrary n the results of Fine for n = 4 [Phys. Rev. Lett. 48, 291 (1982)] and Klyachko et al. for n = 5 [Phys. Rev. Lett. 101, 020403 (2008)], and provides the first complete characterization of a noncontextual polytope with an arbitrary number of settings. In addition, we show that quantum mechanics violates these inequalities for any n \geq 4, and give explicit quantum states and settings with minimal quantum dimension and maximal quantum violation.

View original: http://arxiv.org/abs/1206.3212