Experimental implementation of an eight-dimensional Kochen-Specker set and observation of its connection with the Greenberger-Horne-Zeilinger theorem

TL;DR

This paper experimentally demonstrates an eight-dimensional Kochen-Specker set using single photons, revealing its connection to GHZ states and violating noncontextuality inequalities, thus linking quantum contextuality with nonlocality.

Contribution

The first experimental implementation of an eight-dimensional KS set and its connection to GHZ states, showing violations of noncontextuality inequalities in high-dimensional systems.

Findings

Violates state-independent noncontextuality inequality

Demonstrates connection between contextuality and nonlocality in 8D systems

Shows that certain states violate Mermin-like inequalities

Abstract

For eight-dimensional quantum systems there is a Kochen-Specker (KS) set of 40 quantum yes-no tests that is related to the Greenberger-Horne-Zeilinger (GHZ) proof of Bell's theorem. Here we experimentally implement this KS set using an eight-dimensional Hilbert space spanned by the transverse momentum of single photons. We show that the experimental results of these tests violate a state-independent noncontextuality inequality. In addition, we show that, if the system is prepared in states that are formally equivalent to a three-qubit GHZ and $W$ states, then the results of a subset of 16 tests violate a noncontextuality inequality that is formally equivalent to the three-party Mermin's Bell inequality, but for single eight-dimensional quantum systems. These experimental results highlight the connection between quantum contextuality and nonlocality for eight-dimensional quantum systems.