About testing Bell locality at colliders

TL;DR

This work explores testing Bell locality at colliders by using quantum state tomography to reconstruct spin states of produced particle pairs, enabling witnesses of entanglement and Bell non-locality within an $S$-matrix framework. The key method is to obtain the spin density matrix $\rho$ from angular distributions, express it as $\rho=\tfrac{1}{4}[{\bf1}\otimes{\bf1}+{\cdots}+C_{ij}(\sigma_i\otimes\sigma_j)]$, and analyze polarization and correlations via $\langle\mathcal{O}\rangle={\rm Tr}[\rho\,\mathcal{O}]$, including criteria such as the Horodecki condition $m_1+m_2>1$ for Bell violation. The paper clarifies that collider-based tests are device-dependent and yield Bell non-locality witnesses rather than fully device-independent Bell tests, discusses loopholes (notably super-determinism), and argues that any hidden-variable framework would require new physics or beyond-quantum behavior. It concludes by surveying current collider results showing entanglement and non-locality signals and outlining future collider prospects to extend quantum-information tests to heavier and more complex final states, potentially achieving high-significance observations across multiple processes.

Abstract

High-energy colliders enable the testing of quantum mechanics at its most fundamental level, in the presence of strong and electroweak interactions, with systems that consist of qubits (fermions) and qutrits (massive spin-1 bosons). Quantum state tomography at colliders enables the witnessing of entanglement and Bell non-locality, two defining characteristics of quantum mechanics. We offer a comprehensive explanation of the underlying principles and the methods employed to achieve this remarkable feat.

Figures (2)

• Figure 1: Feynman diagram for the the production of a pair of $\tau$ leptons from electron-positron annihilation.
• Figure 2: Clauser's experimental setup (Stuart Freedman, Berkeley [CC BY-NC 4.0]) and the CMS detector at the LHC (CERN [CC BY-NC 4.0]). Neither is as simple as a falling apple and the device-independence of potential Bell test has to be certified.