# Lab Lunch: 15 October 2019 - Rui Soares Barbosa

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

**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.

### Lab Lunch: 15 October 2019 - Rui Soares Barbosa

MF2 level 4