# Lab Lunch Talk: Acyclicity and Vorob'ev’s theorem: deriving monogamy of non-locality and local macroscopic averages

Speaker: Rui Soares Barbosa

**Abstract:**

Quantum mechanics predicts phenomena that run counter to the usual intuitions from classical physics, e.g. non-locality or contextuality. Not all observables of a quantum system may be measured and be assigned values simultaneously. Rather, contexts of compatible observables provide multiple partial (classical) perspectives on a quantum system: while any two of these fit nicely together, they cannot necessarily be pasted consistently into a global picture. Contextuality, with non-locality as a particular case, arises as this gap between local consistency and global inconsistency.

A natural question is to identify which configurations of contexts allow for
contextuality, and which are inherently classical in the sense that local
consistency implies global consistency. Or in terms more familiar in the
quantum foundations literature: for which measurement scenarios is it the case
that the no-signalling/no-disturbance condition is enough to ensure
classicality, i.e. locality/non-contextuality? An old result due to Vorob'ev,
originally motivated by a problem in game theory, provides a complete
answer to this question. His necessary and sufficient condition turns out to be
equivalent to the well-studied notion of acyclic database schema, which
addressed an analogous concern in the context of relational database theory:
for which database schemata does pairwise projection consistency imply the
existence of a universal relation instance? This will be the theme of the first
part of this talk.

The second part will focus on an application of Vorob'ev’s theorem 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. Note that, as such, no knowledge of quantum
mechanics is assumed (or necessary) for this talk.