Large violations in Kochen Specker contextuality and their applications

Abstract

It is of interest to study how contextual quantum mechanics is, in terms of the violation of Kochen Specker state-independent and state-dependent non-contextuality inequalities. We present state-independent non-contextuality inequalities with large violations, in particular, we exploit a connection between Kochen-Specker proofs and pseudo-telepathy games to show KS proofs in Hilbert spaces of dimension d ≥ 2 17 with the ratio of quantum value to classical bias being O( √ d/ log d). We study the properties of this KS set and show applications of the large violation. It has been recently shown that Kochen-Specker proofs always consist of substructures of state-dependent contextuality proofs called 01-gadgets or bugs. We show a one-to-one connection between 01-gadgets in C d and Hardy paradoxes for the maximally entangled state in C d ⊗ C d . We use this connection to construct large violation 01-gadgets between arbitrary vectors in C d , as well as novel Hardy paradoxes for the maximally entangled state in C d ⊗ C d , and give applications of these constructions. As a technical result, we show that the minimum dimension of the faithful orthogonal representation of a graph in R d is not a graph monotone, a result that that may be of independent interest.