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arXiv:2505.11870 · The European Physical Journal C

Quantum tomography beyond the leading order

J. A. Aguilar–Saavedra

Published Sep 11, 2025• 6 citations
arXivHTMLPDF

Abstract

Abstract Quantum tomography, as a tool to probe foundational aspects of quantum mechanics, relies on extracting spin information from angular distributions. This is inherently a leading-order technique, ill-defined when higher-order corrections are significant. For those cases, we propose to treat higher-order corrections as a background, to be modeled and subtracted from data in the same way as other backgrounds are. We illustrate this procedure for Higgs decays $$H \rightarrow ZZ \rightarrow e^+ e^- \mu ^+ \mu ^-$$ H → Z Z → e + e - μ + μ - , which is of high interest for upcoming qutrit entanglement tests at the Large Hadron Collider.

DOI
10.1140/epjc/s10052-025-14710-z

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Abstract Quantum tomography, as a tool to probe foundational aspects of quantum mechanics, relies on extracting spin information from angular distributions. This is inherently a leading-order technique, ill-defined when higher-order corrections are significant. For those cases, we propose to treat higher-order corrections as a background, to be modeled and subtracted from data in the same way as other backgrounds are. We illustrate this procedure for Higgs decays H→ZZ→e+e−μ+μ−H \rightarrow ZZ \rightarrow e^+ e^- \mu ^+ \mu ^-H→ZZ→e+e−μ+μ− H → Z Z → e + e - μ + μ - , which is of high interest for upcoming qutrit entanglement tests at the Large Hadron Collider.
Quantum tomography in high-energy physics processes has usually been restricted to the spin degrees of freedom. We address the case of top quark decays t → W b , in which the orbital angular momentum ( L ) and the spins of W and b are intertwined into a 54-dimensional LWb density operator. The entanglement between L and the W or b spin is large and could be determined for decays of single top quarks produced at the Large Hadron Collider with Run 2 data. With the foreseen statistical and systematic uncertainties, the significance is well above 5 σ from the separability hypothesis for L - W entanglement, and 3.2 σ for L - b . These would be the first entanglement measurements between orbital and spin angular momenta in high-energy physics. Likewise, the genuine tripartite entanglement between L and the two spins could be established with more than 5 σ . The method presented paves the way for similar measurements in other processes.
Quantum tomography of H→ZZ,WWH \to ZZ, WWH→ZZ,WW beyond leading order
We revisit quantum tomography of H→ZZH \to ZZH→ZZ and H→WWH \to WWH→WW in the presence of higher-order corrections. We verify that neither the use of an effective spin analysing power (only for ZZZZZZ) or a photon veto are sufficient to render the naively-constructed spin density operators physical. A subtraction of higher-order corrections is thus necessary to perform consistent quantum tomography. Such corrections are small when compared to expected experimental uncertainties with current data. As a by-product, we point out the striking possibility to observe parity-violating effects in H→WWH \to WWH→WW.
Quantum tomography is a method to experimentally extract all that is observable about a quantum mechanical system. We introduce quantum tomography to collider physics with the illustration of the angular distribution of lepton pairs. The tomographic method bypasses much of the field-theoretic formalism to concentrate on what can be observed with experimental data. We provide a practical, experimentally driven guide to model-independent analysis using density matrices at every step. Comparison with traditional methods of analyzing angular correlations of inclusive reactions finds many advantages in the tomographic method, which include manifest Lorentz covariance, direct incorporation of positivity constraints, exhaustively complete polarization information, and new invariants free from frame conventions. For example, experimental data can determine the entanglement entropy of the production process. We give reproducible numerical examples and provide a supplemental standalone computer code that implements the procedure. We also highlight a property of complex positivity that guarantees in a least-squares type fit that a local minimum of a χ2\chi ^{2}χ2 statistic will be a global minimum: There are no isolated local minima. This property with an automated implementation of positivity promises to mitigate issues relating to multiple minima and convention dependence that have been problematic in previous work on angular distributions.
We investigate the limitations of the two-qutrit quantum tomography in Higgs-boson decays to four charged leptons. At next-to-leading order, the standard reconstruction can yield an operator that is not positive semidefinite, even when radiatively improved spin-analysing powers are used. We trace this failure to the coherent combination of photon- and Z-mediated contributions to the off-shell dilepton system, whose distinct production and decay structures invalidate the assumed universal decay analysers. Nevertheless, the rank-two angular sector remains accessible and perturbatively stable, enabling a robust lower bound on the squared concurrence, and hence a reliable assessment of entanglement beyond leading order.
Quantum Tomography and Entanglement in Semi-Leptonic h→VV∗h\to VV^*h→VV∗ Decays at Higher Orders
Angular correlations in Higgs decays to electroweak gauge bosons, h→ZZ∗,WW∗h \to ZZ^*, WW^*h→ZZ∗,WW∗, provide a powerful probe of both new physics effects and quantum information observables. We present a systematic study of semi-leptonic Higgs decays h→VV∗→ℓ+ℓ−qqˉh \to V V^* \to \ell^+\ell^- q\bar{q}h→VV∗→ℓ+ℓ−qqˉ​ and ℓ±νℓqqˉ′\ell^\pm ν_\ell q\bar{q}'ℓ±νℓ​qqˉ​′, including finite final state fermion masses, NLO QCD, and NLO electroweak corrections. We show that finite final state quark masses can induce effects that go beyond the two-qutrit description in more inclusive regimes, while remaining controllable with suitable kinematic selections. QCD corrections lead to modest percent-level shifts, whereas electroweak corrections can significantly modify the angular structure, particularly in the h→ZZ∗h\to ZZ^*h→ZZ∗ channels. We assess the impact of these effects on the reconstructed density matrix and entanglement measures, finding that, although they modify the angular observables, the semi-leptonic channels are better approximated by a two-qutrit description than the fully leptonic decay h→e+e−μ+μ−h\to e^+e^-μ^+μ^-h→e+e−μ+μ−.
In recent years, an interest in the study of quantum information has grown within the high-energy particle physics community. The possibility to establish the presence of entanglement at particle colliders, such as the Large Hadron Collider (LHC) at CERN, is a novel and thrilling research direction, offering the opportunity to push quantum mechanics to its limits by using the heaviest fundamental particle: the top quark. With this in mind, we propose to use measurements of quantum entanglement to probe the behaviour of fundamental interactions and to search for New Physics at high energy within the Standard Model Effective Field Theory paradigm. Inspired by recent proposals to measure entanglement of top quark pairs produced at the LHC, we examine how the existence of new interactions between fundamental particles modify the Standard Model expectations. By performing analytical calculations, we unveil a non-trivial pattern of effects depending on the kinematical phase space configurations.