The Elegant Joint Quantum Measurement and some conjectures about N-locality in the Triangle and other Configurations

Understand

In order to study N-locality without inputs in long lines and in configurations with loops, e.g.

• the triangle, we introduce a natural joint measurement on two qubits different from the usual Bell state measurement.
• The resulting quantum probability $p(a_1,a_2,...,a_N)$ has interesting features.
• In particular the probability that all results are equal is that large, while respecting full symmetry, that it seems highly implausible that one could reproduce it with any N-local model, though - unfortunately - I have not been unable to prove it.