Quantum information with top quarks in QCD

TL;DR

This paper explores the quantum entanglement and Bell inequality violations in top-antitop quark pairs produced in high-energy QCD processes, proposing experimental observables and extending quantum tomography protocols for collider experiments.

Contribution

It provides a comprehensive framework for analyzing the quantum state of top quark pairs in collider environments, including entanglement detection and quantum state reconstruction methods.

Findings

Entanglement and CHSH violation are present in QCD-produced top pairs.

Experimental observables for detecting quantum correlations are identified.

Quantum tomography protocols are extended to general states and production mechanisms.

Abstract

Top quarks represent unique high-energy systems since their spin correlations can be measured, thus allowing to study fundamental aspects of quantum mechanics with qubits at high-energy colliders. We present here the general framework of the quantum state of a top-antitop ($t\bar{t}$) quark pair produced through quantum chromodynamics (QCD) in a high-energy collider. We argue that, in general, the total quantum state that can be probed in a collider is given in terms of the production spin density matrix, which necessarily gives rise to a mixed state. We compute the quantum state of a $t\bar{t}$ pair produced from the most elementary QCD processes, finding the presence of entanglement and CHSH violation in different regions of phase space. We show that any realistic hadronic production of a $t\bar{t}$ pair is a statistical mixture of these elementary QCD processes. We focus on the experimentally relevant cases of proton-proton and proton-antiproton collisions, performed at the LHC and the Tevatron, analyzing the dependence of the quantum state with the energy of the collisions. We provide experimental observables for entanglement and CHSH-violation signatures. At the LHC, these signatures are given by the measurement of a single observable, which in the case of entanglement represents the violation of a Cauchy-Schwarz inequality. We extend the validity of the quantum tomography protocol for the $t\bar{t}$ pair proposed in the literature to more general quantum states, and for any production mechanism. Finally, we argue that a CHSH violation measured in a collider is only a weak form of violation of Bell's theorem, necessarily containing a number of loopholes.