Spin-bounded correlations: rotation boxes within and beyond quantum theory

TL;DR

This paper introduces 'rotation boxes' to analyze how detector click probabilities respond to spatial rotations in various theories, revealing quantum limits and beyond-quantum advantages in spin correlations with foundational and practical implications.

Contribution

It provides a comprehensive mathematical framework for rotation correlations, characterizes quantum and beyond-quantum spin correlations, and explores applications in quantum information and spacetime physics.

Findings

Quantum theory admits the most general rotational correlations for spins 0, 1/2, and 1.

Beyond-quantum resources of spin 3/2 outperform quantum resources in a metrological game.

An exact convex characterization of spin-1 correlations and a Tsirelson-type inequality for spins 3/2 and higher.

Abstract

How can detector click probabilities respond to spatial rotations around a fixed axis, in any possible physical theory? Here, we give a thorough mathematical analysis of this question in terms of "rotation boxes", which are analogous to the well-known notion of non-local boxes. We prove that quantum theory admits the most general rotational correlations for spins 0, 1/2, and 1, but we describe a metrological game where beyond-quantum resources of spin 3/2 outperform all quantum resources of the same spin. We prove a multitude of fundamental results about these correlations, including an exact convex characterization of the spin-1 correlations, a Tsirelson-type inequality for spins 3/2 and higher, and a proof that the general spin-J correlations provide an efficient outer SDP approximation to the quantum set. Furthermore, we review and consolidate earlier results that hint at a wealth of applications of this formalism: a theory-agnostic semi-device-independent randomness generator, an exact characterization of the quantum (2,2,2)-Bell correlations in terms of local symmetries, and the derivation of multipartite Bell witnesses. Our results illuminate the foundational question of how space constrains the structure of quantum theory, they build a bridge between semi-device-independent quantum information and spacetime physics, and they demonstrate interesting relations to topics such as entanglement witnesses, spectrahedra, and orbitopes.