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abstract: 'Measurements on entangled quantum states can produce outcomes that are nonlocally correlated. But according to Tsirelson’s theorem, there is a quantitative limit on quantum nonlocality. It is interesting to explore what would happen if Tsirelson’s bound were violated. To this end, we consider a model that allows arbitrary nonlocal correlations, colloquially referred to as “box world”. We show that while box world allows more highly entangled states than quantum theory, measurements in box world are rather limited. As a consequence there is no entanglement swapping, teleportation or dense coding.'
author:
- 'Anthony J. Short$^1$'
- Jonathan Barrett$^2$
title: ' Strong nonlocality: A trade-off between states and measurements '
---

Introduction
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Despite its great explanatory and predictive power, the standard formalism of quantum theory - in which states are represented by vectors in a complex Hilbert space - retains an abstract mathematical character. Of course there is no reason why Nature should not be described by an abstract mathematical formalism. But it is notable that in quantum theory textbooks, the formalism is simply postulated. It is not, say, derived from a small set of elementary physical considerations in the manner of special relativity. This invites the question: why 