[Paper Review] When the Machine Chimes the Bell: Entanglement and Bell Inequalities with Boosted $t\bar{t}$

Zhongtian Dong, Dorival Gonçalves+2 more|arXiv (Cornell University)|May 11, 2023

Particle physics theoretical and experimental studies66 references4 citations

TL;DR

This paper proposes a novel method to probe quantum entanglement and Bell inequality violations in top quark pair ($t\bar{t}$) production at the LHC using the semi-leptonic decay channel with boosted top quarks. By combining jet substructure techniques, machine learning-based quark-tagging, and an optimal hadronic polarimeter, the authors demonstrate that entanglement can be observed above 5σ significance with existing data, and Bell inequality violations may be detected above 4σ at the HL-LHC with 3 ab⁻¹ of integrated luminosity.

ABSTRACT

The Large Hadron Collider provides a unique opportunity to study quantum entanglement and violation of Bell inequalities at the highest energy available today. In this paper, we will investigate these quantum correlations with top quark pair production, which represents a system of two-qubits. The spacelike separation requirement for the two causally disconnected top quarks requires they fly relativistically away from each other, which motivates the use of the boosted top-tagging with the semi-leptonic top pair channel. Although measuring the spin polarization of the hadronic top quark is known to be challenging, our study indicates that it is feasible to reconstruct the spin density matrix of the two-qubit system using an optimal hadronic polarimeter. This is achieved with the aid of jet substructure techniques and NN-inspired reconstruction methods, which improve the mapping between subjets and quarks. We find that entanglement can already be observed at more than $5σ$ level with existing data, and violation of Bell inequalities may be probed above 4$σ$ level at the HL-LHC with 3 ab$^{-1}$ of data.

Motivation & Objective

• To investigate quantum entanglement and Bell inequality violations in high-energy $t\bar{t}$ pairs produced at the LHC, leveraging the unique conditions of boosted top quarks.
• To overcome the challenge of reconstructing spin correlations in the semi-leptonic channel, which offers higher statistics than the dilepton channel but poses greater reconstruction difficulties.
• To develop a robust method for reconstructing the spin density matrix of the two-qubit $t\bar{t}$ system using an optimal hadronic polarimeter and advanced jet substructure techniques.
• To assess the feasibility of observing spacelike-separated top quark decays, a necessary condition for loophole-free Bell tests, in the boosted regime.

Proposed method

• The study employs the semi-leptonic $t\bar{t}$ decay channel to increase signal statistics by a factor of six compared to the dilepton channel.
• Jet substructure techniques are used to identify and reconstruct the hadronic decay products of top quarks, improving the mapping between subjets and quarks.
• A neural network-inspired reconstruction method enhances the fidelity of quark tagging, enabling more accurate spin state reconstruction.
• An optimal hadronic polarimeter is constructed to measure the spin density matrix of the two-qubit system, minimizing reconstruction bias.
• The unfolding procedure uses Tikhonov regularization with singular value decomposition to invert detector response matrices and extract true distributions of spin correlation observables.
• Statistical significance is evaluated using error propagation through the full covariance matrix of unfolded distributions, accounting for bin-to-bin correlations and Monte Carlo response matrix uncertainties.

Figure 3: Entanglement ( $\mathcal{E}$ ) and Bell inequalities measure ( $\mathcal{B}_{1},\mathcal{B}_{2}$ ) (at parton-level) as a function of $m_{tt}$ and spacelike separation probability. The latter refers to the fraction of $t$ and $\bar{t}$ decays that are spacelike-separated. We impose $|\cos\

Experimental results

Research questions

• RQ1 Can quantum entanglement in top quark pairs be observed with existing LHC data using the semi-leptonic decay channel and boosted kinematics?
• RQ2 To what extent can Bell inequality violations be probed at the HL-LHC with 3 ab⁻¹ of integrated luminosity using the proposed reconstruction techniques?
• RQ3 Is it feasible to reconstruct the spin density matrix of the $t\bar{t}$ system with sufficient accuracy to test non-classical correlations in the boosted regime?
• RQ4 How does the fraction of spacelike-separated $t\bar{t}$ decays vary with invariant mass, and what is its impact on the viability of loophole-free Bell tests?
• RQ5 What role do jet substructure and machine learning play in improving the reconstruction of top quark spin states in the hadronic decay channel?

Key findings

• Entanglement in $t\bar{t}$ pairs can be observed at more than 5σ significance level using existing LHC data, thanks to improved reconstruction in the semi-leptonic channel.
• Violation of Bell inequalities may be probed at more than 4σ significance level at the HL-LHC with 3 ab⁻¹ of integrated luminosity.
• The fraction of spacelike-separated $t\bar{t}$ decays exceeds 90% for invariant masses above 800 GeV, satisfying a key condition for testing non-locality.
• The use of an optimal hadronic polarimeter combined with jet substructure and machine learning enables accurate reconstruction of the spin density matrix, even in complex hadronic environments.
• The unfolding algorithm with Tikhonov regularization and SVD-based inversion successfully mitigates detector effects and preserves statistical correlations in the spin correlation observables.
• The analysis accounts for both statistical uncertainties and Monte Carlo response matrix errors through 100 pseudo-experiments, ensuring robust significance estimation.

Figure 4: Differential angular distributions with respect to $\cos\theta^{i}_{\ell}\cos\bar{\theta}^{i}_{q_{\text{opt}}}$ for $i=k$ (left), $i=r$ (middle) and $i=n$ (right). We display the parton level correlations between the charged lepton and down-type quark (black dashed), and charge lepton with