Testing Bell inequalities in Higgs boson decays

TL;DR

This paper explores the potential to test Bell inequalities using Higgs boson decays into W boson pairs, proposing methods for experimental reconstruction and analyzing the likelihood of observing quantum nonlocality violations.

Contribution

It introduces a method to reconstruct the W boson spin density matrix from decay products and evaluates the feasibility of measuring Bell inequality violations in collider experiments.

Findings

CGLMP inequality is nearly maximally violated in simulations.

Violation of the generalized CHSH inequality is unlikely to be measurable.

Experimental tests could be feasible with current collider datasets.

Abstract

Higgs boson decays produce pairs of $W$ bosons in a maximally entangled state, the spins of which can be expected to violate Bell inequalities. We show that the spin density matrix of the $W^\pm$ pair may be reconstructed experimentally from the directions of the charged lepton decay products, and from it the expectation values of various Bell operators determined. Numerical simulations of $H\rightarrow WW^*$ decays indicate that violation of a generalised CHSH inequality is unlikely to be measurable, however the CGLMP inequality is near-maximally violated. Experimental Bell tests could be performed at a variety of colliders and in different production channels. If reconstruction effects and backgrounds can be controlled then statistically significant violations could be observable even with datasets comparable to those already collected at the LHC.