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In order to study N-locality without inputs in long lines and inconfigurations with loops, e.g. the triangle, we introduce a natural jointmeasurement on two qubits different from the usual Bell state measurement. Theresulting quantum probability $p(a_1,a_2,...,a_N)$ has interesting features. Inparticular the probability that all results are equal is that large, whilerespecting full symmetry, that it seems highly implausible that one couldreproduce it with any N-local model, though - unfortunately - I have not beenunable to prove it.

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