Quantum information with top quarks in QCD

• URL: http://arxiv.org/abs/2203.05582v2
• Date: Tue, 20 Sep 2022 18:00:02 GMT
• Title: Quantum information with top quarks in QCD
• Authors: Yoav Afik and Juan Ram\'on Mu\~noz de Nova
• Abstract summary: We present the general framework of the quantum state of a top-antitop ($tbart$) quark pair produced through quantum chromodynamics (QCD) in a high-energy collider. We show that any realistic hadronic production of a $tbart$ pair is a statistical mixture of these elementary QCD processes. We provide experimental observables for entanglement and CHSH-violation signatures.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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