Theory-independent randomness generation from spatial symmetries

TL;DR

This paper reveals that the structure of quantum correlations in a rotational scenario can be derived solely from spatial symmetries, enabling a theory-independent approach to randomness generation and supporting the idea that space-time symmetries shape quantum probabilistic structures.

Contribution

It introduces a semi-device-independent scheme linking spatial symmetries to quantum correlations, enabling theory-independent randomness certification.

Findings

Quantum correlations are determined by spatial covariance alone.

A protocol for secure, theory-independent randomness generation is proposed.

The results support the idea that space-time symmetries influence quantum probabilistic structures.

Abstract

We demonstrate a fundamental relation between the structures of physical space and of quantum theory: the set of quantum correlations in a rotational prepare-and-measure scenario can be derived from covariance alone, without assuming quantum physics. To show this, we consider a semi-device-independent randomness generation scheme where one of two spatial rotations is performed on an otherwise uncharacterized preparation device, and one of two possible measurement outcomes is subsequently obtained. An upper bound on a theory-independent notion of spin is assumed for the transmitted physical system. It turns out that this determines the set of quantum correlations and the amount of certifiable randomness in this setup exactly. Interestingly, this yields the basis of a theory-independent protocol for the secure generation of random numbers. Our results support the conjecture that the symmetries of space and time determine at least part of the probabilistic structure of quantum theory.