Super quantum probabilities and three-slit experiments -- Wright's pentagon state and the Popescu-Rohrlich box require third-order interference

Understand

Quantum probabilities differ from classical ones in many ways, e.g., by violating the well-known Bell and CHSH inequalities or another simple inequality due to R.

• Wright.
• The latter one has recently regained attention because of its equivalence to a novel noncontextual inequality by Klyachko et al.
• On the other hand, quantum probabilities still obey many limitations which need not hold any more in more general probabilistic theories (super quantum probabilities).