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 ≥ 217 with the ratio of quantum value to classical bias being O(d/logd) . 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. We show a one-to-one connection between 01-gadgets in Cd and Hardy paradoxes for the maximally entangled state in Cd-Cd . We use this connection to construct large violation 01-gadgets between arbitrary vectors in Cd, as well as novel Hardy paradoxes for the maximally entangled state in Cd-Cd, 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 Rd is not a graph monotone, a result that may be of independent interest.