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### Rui Soares Barbosa

INL – International Iberian Nanotechnology Institute, Portugal, rui.soaresbarbosa@inl.int

### From Vorob'ev’s theorem to monogamy of non-locality and local macroscopic averages

Vorob'ev’s theorem characterises those configurations of contexts (i.e. measurement scenarios) which are
inherently classical in the sense that the no-signalling or no-disturbance condition is enough to ensure
locality or non-contextuality. Even if at first glance these scenarios may look a bit boring from the point of
view of contextuality, we will discuss how Vorob'ev’s result can be applied to provide an elegant structural
explanation for two related phenomena: (1) monogamy of non-locality, which establishes a trade-off
between strength of non-locality shared between a party and multiple others, and (2) locality of average
macroscopic behaviour, regardless of the non-classicality present in the microscopic state of a system.
Since Vorob'ev’s theorem depends solely on the compatibility structure of measurements, these results
hold not just for quantum theory, but for any empirical behaviours satisfying only the no-signalling
condition.