Universal violation of pentagon inequalities in four-state systems

TL;DR

This paper demonstrates that in four-state quantum systems, a set of 60 real vectors derived from a 600-cell structure universally violate pentagon inequalities, highlighting fundamental contextuality in quantum mechanics.

Contribution

It introduces a comprehensive set of 60 vectors that densely cover four-dimensional Hilbert space, showing universal violation of pentagon inequalities by quantum mechanics.

Findings

Quantum states violate pentagon inequalities universally

The 60 vectors densely cover Hilbert space

Presence of N-gons relevant to contextuality demonstrations

Abstract

The 60 real vectors derived from the vertices of a 600-cell are shown to yield a number of pentagon inequalities that are satisfied by realistic noncontextual theories but violated by quantum mechanics. The replicas of these inequalities cover Hilbert space so densely that every real four-dimensional vector violates at least one of them. It is pointed out that this set of 60 vectors contains numerous "N-gons" (generalizations of pentagons) that may be of interest in connection with demonstrations of contextuality.