The uncertainty principle determines the non-locality of quantum mechanics

TL;DR

This paper establishes a fundamental quantitative connection between the uncertainty principle and non-locality in quantum mechanics, showing that the degree of non-locality is constrained by these two core features.

Contribution

It reveals that the uncertainty principle and non-locality are intrinsically linked, and that non-locality is limited by the strength of the uncertainty principle and steering across all physical theories.

Findings

Non-locality cannot be increased without respecting the uncertainty principle.

The degree of non-locality is determined by the uncertainty principle and steering.

The link between uncertainty and non-locality applies universally to all physical theories.

Abstract

Two central concepts of quantum mechanics are Heisenberg's uncertainty principle, and a subtle form of non-locality that Einstein famously called ``spooky action at a distance''. These two fundamental features have thus far been distinct concepts. Here we show that they are inextricably and quantitatively linked. Quantum mechanics cannot be more non-local with measurements that respect the uncertainty principle. In fact, the link between uncertainty and non-locality holds for all physical theories.More specifically, the degree of non-locality of any theory is determined by two factors -- the strength of the uncertainty principle, and the strength of a property called ``steering'', which determines which states can be prepared at one location given a measurement at another.