Operational witnesses of non-classicality via Bell inequalities and contextuality

Abstract

This thesis investigates operational signatures of non-classicality in quantum systems, examining the relationship between Bell inequalities, contextuality tests, and discrete Wigner negativity across four case studies. The first analyzes multipartite entanglement and genuine multipartite nonlocality in multiqubit systems, deriving analytical expressions for Svetlichny inequality violations for generalized Greenberger–Horne–Zeilinger (GHZ) and maximal-slice states; the results indicate that the entanglement–nonlocality relationship depends on state structure rather than scalar entanglement measures alone. The second uses an optimized Bell inequality as a contextuality witness for the spin-1 quantum kicked top, revealing correlations between violation strength and the regular-versus-chaotic structure of the classical phase space. The third examines two qutrit Unruh–DeWitt detectors coupled to the Minkowski vacuum, showing that an initially noncontextual product state can develop contextual correlations through vacuum-mediated interactions, with contextuality onset coinciding with discrete Wigner negativity. The fourth constructs logical Bell inequalities for odd prime dimensions that connect single-qudit Wigner negativity to inequality violation. Each of these tests constrains a different class of classical model: locally causal hidden variables, noncontextual hidden variables, or positive Wigner representations. A recurring theme is that a violation of such an inequality certifies a property of the observed measurement statistics, rather than directly quantifying an underlying quantum resource.