# Semi-device-independent information processing with spatiotemporal degrees of freedom

## TL;DR

This paper explores how spatiotemporal degrees of freedom influence nonlocal correlations in quantum devices, establishing symmetry constraints and enabling semi-device-independent certification of nonlocality with fewer measurements.

## Contribution

It introduces a symmetry-based framework for analyzing bipartite quantum correlations with spatiotemporal inputs, providing new Bell witnesses and semi-device-independent protocols.

## Key findings

- Correlations respect input symmetries without assuming quantum theory
- Pure correlations must be nonlocal, noisy ones can be explained by local models
- Bell witnesses can certify nonlocality with fewer measurements

## Abstract

Nonlocality, as demonstrated by the violation of Bell inequalities, enables device-independent cryptographic tasks that do not require users to trust their apparatus. In this article, we consider devices whose inputs are spatiotemporal degrees of freedom, e.g. orientations or time durations. Without assuming the validity of quantum theory, we prove that the devices' statistical response must respect their input's symmetries, with profound foundational and technological implications. We exactly characterize the bipartite binary quantum correlations in terms of local symmetries, indicating a fundamental relation between spacetime and quantum theory. For Bell experiments characterized by two input angles, we show that the correlations are accounted for by a local hidden variable model if they contain enough noise, but conversely must be nonlocal if they are pure enough. This allows us to construct a "Bell witness" that certifies nonlocality with fewer measurements than possible without such spatiotemporal symmetries, suggesting a new class of semi-device-independent protocols for quantum technologies.