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arXiv:2407.01672 · Physical review. D/Physical review. D.

Optimizing entanglement and Bell inequality violation in top antitop events

Kun Cheng, Tao Han, Matthew Low

Published Feb 19, 2025• 28 citations
arXivHTMLPDF

Abstract

A top quark and an antitop quark produced together at colliders have correlated spins. These spins constitute a quantum state that can exhibit entanglement and violate Bell’s inequality. In realistic collider experiments, most analyses allow the axes, as well the Lorentz frame, to vary event by event, thus introducing a dependence on the choice of event-dependent basis leading us to adopt “fictitious states,” rather than genuine quantum states. The basis dependence of fictitious states allows for an optimization procedure, which makes the usage of fictitious states advantageous in measuring entanglement and Bell inequality violation. In this work, we show analytically that the basis that diagonalizes the spin-spin correlations is optimal for maximizing spin correlations, entanglement, and Bell inequality violation. We show that the optimal basis is approximately the same as the fixed beam basis (or the rotated beam basis) near the t t ¯ production threshold, while it approaches the helicity basis far above threshold. Using this basis, we present the sensitivity for entanglement and Bell inequality violation in t t ¯ events at the Large Hadron Collider (LHC) and a future e + e − collider. Since observing Bell inequality violation appears to be quite challenging experimentally, and requires a large dataset in collider experiments, choosing the optimal basis is crucially important to observe Bell inequality violation. Our method and general approach are equally applicable to other systems beyond t t ¯ , including interactions beyond the Standard Model.

DOI
10.1103/physrevd.111.033004

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A top quark and an antitop quark produced together at colliders have correlated spins. These spins constitute a quantum state that can exhibit entanglement and violate Bell’s inequality. In realistic collider experiments, most analyses allow the axes, as well the Lorentz frame, to vary event by event, thus introducing a dependence on the choice of event-dependent basis leading us to adopt “fictitious states,” rather than genuine quantum states. The basis dependence of fictitious states allows for an optimization procedure, which makes the usage of fictitious states advantageous in measuring entanglement and Bell inequality violation. In this work, we show analytically that the basis that diagonalizes the spin-spin correlations is optimal for maximizing spin correlations, entanglement, and Bell inequality violation. We show that the optimal basis is approximately the same as the fixed beam basis (or the rotated beam basis) near the t t ¯ production threshold, while it approaches the helicity basis far above threshold. Using this basis, we present the sensitivity for entanglement and Bell inequality violation in t t ¯ events at the Large Hadron Collider (LHC) and a future e + e − collider. Since observing Bell inequality violation appears to be quite challenging experimentally, and requires a large dataset in collider experiments, choosing the optimal basis is crucially important to observe Bell inequality violation. Our method and general approach are equally applicable to other systems beyond t t ¯ , including interactions beyond the Standard Model.
There is a significant interest in testing quantum entanglement and Bell inequality violation in high-energy experiments. Since the analyses in high-energy experiments are performed with events statistically averaged over phase space, the states used to determine observables depend on the choice of coordinates through an event-dependent basis and are thus not genuine quantum states, but rather “fictitious states.” We find that the basis which diagonalizes the spin-spin correlations is optimal for constructing fictitious states to test the violation of Bell’s inequality. This result is applied directly to the bipartite qubit system of a top and antitop produced at a hadron collider. We show that the beam axis is the optimal basis choice near the tt¯ threshold production for measuring Bell inequality violation, while at high transverse momentum the basis that aligns along the momentum direction of the top is optimal. Published by the American Physical Society 2024
Correlations between the spins of top-quark pairs produced at a collider can be used to probe quantum entanglement at energies never explored so far. We show how the measurement of a single observable can provide a test of the violation of a Bell inequality at the 98% C.L. with the statistical uncertainty of the data already collected at the Large Hadron Collider, and at the 99.99% C.L. with the higher luminosity of the next run. Detector acceptance, efficiency, and migration effects are taken into account. The test relies on the spin correlations alone and does not require the determination of probabilities-in contrast to all other tests of Bell inequalities.
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 semileptonic top pair channel has a factor of 6 increase in statistics and easier reconstruction with respect to the dileptonic 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 the 5 σ level with existing data, and violation of Bell inequalities may be probed above the 4 σ level at the HL-LHC with 3 ab − 1 of data. Published by the American Physical Society 2024
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 ( tt¯ ) 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 tt¯ 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 tt¯ 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 tt¯ 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.
A bstract Quantum entanglement is a fundamental property of quantum mechanics. Recently, studies have explored entanglement in the tt‾ t\overline{t} tt t t ¯ system at the Large Hadron Collider (LHC) when both the top quark and anti-top quark decay leptonically. Entanglement is detected via correlations between the polarizations of the top and anti-top and these polarizations are measured through the angles of the decay products of the top and anti-top. In this work, we propose searching for evidence of quantum entanglement in the semi-leptonic decay channel where the final state includes one lepton, one neutrino, two b -flavor tagged jets, and two light jets from the W decay. We find that this channel is both easier to reconstruct and has a larger effective quantity of data than the fully leptonic channel. As a result, the semi-leptonic channel is 60% more sensitive to quantum entanglement and a factor of 3 more sensitive to Bell inequality violation, compared to the leptonic channel. In 139 fb − 1 (3 ab −1 ) of data at the LHC (HL-LHC), it should be feasible to measure entanglement at a precision of ≲ 3% (0 . 7%). Detecting Bell inequality violation, on the other hand, is more challenging. With 300 fb −1 (3 ab −1 ) of integrated luminosity at the LHC Run-3 (HL-LHC), we expect a sensitivity of 1 . 3 σ (4 . 1 σ ). In our study, we utilize a realistic parametric fitting procedure to optimally recover the true angular distributions from detector effects. Compared to unfolding this procedure yields more stable results.
Tests of quantum properties of fundamental particles in high energy colliders are starting to appear. Entanglement and Bell inequality violation in top and antitop quark system is of particular interest since top quarks are unstable particles that undergo a cascade decay. We argue for criteria for the spacelike separation between top and antitop quarks at their different decay stages. We considered causal separation at three different instances: at the top quark decay, at the W boson decay, and at the lepton/jet contact with the macroscopic apparatus. We showed that the spacelike fraction of events is the smallest, when requiring that both top quarks and W bosons decay within the spacelike interval. For high invariant masses, typically required for the Bell inequality violation, this is almost identical to just the top quark decay requirement. We also include an option for the angular correlation of the b quarks from top quark decay to be used for the spin correlation measurement. We require that both top quark and b hadron decays are spacelike separated. Again, we find that at high invariant masses it is almost identical to just the requirement of spacelike separation between top and antitop quarks. We provide numerical values for our proposed criteria. If such a criterion is satisfied, the system is guaranteed to not be in a causal connection.