Universal violation of pentagon inequalities in four-state systems

Details Universal violation of pentagon inequalities in four-state systems Universal violation of pentagon inequalities in four-state systems

2011-11-21

arxiv.org/abs/1111.4713v1

Physics

Quantum Physics

8 pages, 5 tables

Scientific paper

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.

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