Reformulating noncontextuality inequalities in an operational approach

A new theory-independent noncontextuality inequality is presented [R. Kunjwal and R. W. Spekkens, Phys. Rev. Lett. 115, 110403 (2015)] based on a Kochen-Specker (KS) set without imposing the assumption of determinism. By proposing noncontextuality inequalities, we show that such result can be generalized from a KS set to the noncontextuality inequalities not only for a state-independent scenario but also for a state-dependent scenario. The YO-13 ray and $n$ cycle ray are considered as examples.

Figure 1

The YO-13-ray graph.

Figure 2

The original KCBS graph (a) and the one (b) after adding new vertices $A,B,C,D,E$.

Figure 3

The $n$ cycle graph after adding new vertices $1^{\prime },2^{\prime },...,n^{\prime }$.