⚛️ phenomenology

Quantum Information in High-Energy Physics: a top subject

This award-winning paper reviews the application of Quantum Information techniques to High-Energy Physics, focusing on the top quark as a relativistic qubit to demonstrate how experimental protocols for quantum tomography led to the highest-energy observations of entanglement by the ATLAS and CMS collaborations, thereby establishing a rich new field of QI in HEP.

Original authors: Yoav Afik, Juan Ramón Muñoz de Nova

Published 2026-10-02

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Yoav Afik, Juan Ramón Muñoz de Nova

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Deep within the heart of modern physics lie two distinct worlds that rarely speak to one another. On one side stands the study of the very small, where particles behave in ways that defy common sense, such as being in two places at once or sharing a secret connection that transcends distance. On the other side stands the study of the very heavy and fast, where scientists smash particles together at speeds close to the limit of light to recreate the conditions of the early universe. For decades, these fields operated in isolation, with the first focusing on information and the second on fundamental forces. Yet, a new perspective suggests that the most extreme environments in the universe might actually be the perfect laboratories to test the strangest rules of quantum mechanics. The key to unlocking this connection lies in understanding how particles can become linked, a phenomenon where the state of one particle instantly influences another, no matter how far apart they are. This link is not just a theoretical curiosity; it is the foundation of a new era of technology and a deeper understanding of reality itself.

A team of researchers has now successfully bridged this gap, demonstrating that the highest-energy collisions ever created by human hands can serve as a stage for these quantum connections. Their work focuses on a specific particle known as the top quark, the heaviest of all known fundamental particles. When these particles are created in the massive particle accelerators at the Large Hadron Collider, they do not appear alone; they are born in pairs, one being the top quark and the other its antimatter twin, the antitop quark. The researchers proposed that these pairs are not just random debris from a collision but are actually entangled, meaning their spins—their intrinsic angular momentum—are locked together in a way that cannot be explained by classical physics. To prove this, they developed a method to read the quantum state of these fleeting particles, a process akin to taking a complete three-dimensional photograph of a ghost that vanishes before it can be touched.

The challenge in observing such a phenomenon is immense. The top quark is so unstable that it decays, or breaks apart, in a fraction of a second, far too quickly for any detector to track its spin directly. However, the researchers realized that the top quark leaves a perfect record of its spin in the direction of the particles it creates when it decays. By analyzing the paths of these decay products, specifically the leptons, the team could reconstruct the original quantum state of the top-antitop pair. They designed a protocol to measure the correlation between the directions of these decay products, effectively performing a quantum tomography, which is a technique used to map out the full quantum state of a system. This approach allowed them to translate the abstract language of quantum information into concrete measurements that the detectors at the Large Hadron Collider could actually record.

The results of this theoretical proposal were confirmed by two major experimental collaborations, ATLAS and CMS, using data from the Large Hadron Collider. By focusing on the specific conditions where the top quarks are created with just enough energy to form a pair, the researchers found a clear signal of entanglement. The data showed that the spins of the top and antitop quarks were correlated in a way that violated the limits of classical physics, confirming that they were indeed entangled. This observation was not a marginal finding; the statistical certainty was so high that it ruled out any chance of the result being a fluke. It stands as the highest-energy observation of quantum entanglement ever recorded, pushing the boundary of where these quantum effects can be seen from the microscopic realm of atoms to the subatomic realm of high-energy collisions.

This discovery does more than just confirm a prediction; it opens a new door for physics. By treating the top quark as a reliable test subject, or a "fruit fly" of the relativistic world, scientists now have a powerful tool to explore the fundamental nature of reality at energies previously thought inaccessible. The work establishes a clear dictionary that translates concepts from quantum information science into the language of high-energy physics, allowing researchers to use the massive machines of particle physics to answer questions about the nature of information and connection. It suggests that the universe, even in its most violent and energetic moments, adheres to the subtle and counterintuitive rules of quantum mechanics. The success of this project has already inspired a wave of new research, with scientists now looking to apply these same techniques to other particles and even searching for new physics beyond our current understanding, proving that the study of the very small and the very fast are now inextricably linked.

Technical Summary: Quantum Information in High-Energy Physics: a top subject

Problem Statement
While Quantum Information (QI) theory has advanced significantly, its application to High-Energy Physics (HEP) has been limited, particularly regarding experimental studies of fundamental quantum features like entanglement. Although theoretical works have addressed entanglement in relativistic quantum field theories (ranging from proton composition to black hole radiation), there is a lack of a precise "dictionary" to translate QI concepts into HEP observables and vice versa. Furthermore, identifying feasible HEP platforms for implementing QI protocols has remained a challenge. The authors aim to bridge this gap by demonstrating how QI techniques can be implemented in high-energy colliders, specifically focusing on the top quark as a paradigmatic relativistic qubit.

Methodology
The paper establishes a formal framework to describe high-energy particle production as a quantum information problem:

Formalism Translation: The authors define the production of a particle-antiparticle pair ( $P\bar{P}$ ) as a two-qubit system. They derive the production spin density matrix ( $\rho$ ) from scattering amplitudes, normalizing it by the differential cross-section. This matrix is decomposed into spin polarizations ( $B^\pm$ ) and a spin correlation matrix ( $C$ ), analogous to the Bloch vector and correlation tensor in standard qubit systems.
Entanglement Criteria: The study utilizes standard QI metrics adapted for HEP, including the Peres-Horodecki criterion (partial transpose), concurrence ( $C[\rho]$ ), and entanglement witnesses. Specifically, they define a witness $\Delta$ based on the correlation matrix elements, where $\Delta > 0$ signals entanglement.
Theoretical Calculation: The authors calculate these quantities for top-antitop ( $t\bar{t}$ ) production via Quantum Chromodynamics (QCD) at Leading Order (LO). They analyze two primary production channels: quark-antiquark ( $q\bar{q}$ ) annihilation and gluon-gluon ($gg$) fusion. The calculations are performed in the center-of-mass frame using the helicity basis, parameterized by the invariant mass ( $M_{t\bar{t}}$ ) and the top quark velocity ( $\beta$ ).
Experimental Protocol: Recognizing the top quark's unique properties—specifically its large mass ( $m_t \approx 172.5$ GeV) and extremely short lifetime ( $\tau_t \approx 4.6 \times 10^{-25}$ s)—the authors propose a quantum tomography protocol. Because the top quark decays before hadronization or spin decorrelation can occur, its spin information is imprinted on the angular distribution of its decay products. For dileptonic decays ( $t\bar{t} \to b\ell^+\nu \bar{b}\ell^-\bar{\nu}$ ), the angular correlation between the leptons directly maps to the spin correlation matrix $C$ .
Witness Simplification: To facilitate experimental measurement, the authors propose a simplified entanglement witness based on the fidelity with respect to the spin singlet state. This reduces the requirement to measuring a single parameter, $D = \text{Tr}[C]/3$ , which is directly extractable from the angular separation ( $\phi$ ) of the leptons via the relation $D = -3\langle \cos \phi \rangle$ .

Key Contributions

Interdisciplinary Bridge: The work provides a rigorous dictionary translating QI concepts (density matrices, entanglement, tomography) into HEP observables (cross-sections, spin correlations, kinematic variables).
Top Quark as a Relativistic Qubit: The paper identifies the top quark as a "drosophila" (model organism) for relativistic qubits due to its polarimetric properties and lack of spin decoherence prior to decay.
Analytical Results: The authors provide analytical expressions for the concurrence of $t\bar{t}$ pairs produced via $q\bar{q}$ and $gg$ channels, identifying specific regions in phase space (near threshold and high transverse momentum) where entanglement is maximal.
Experimental Proposal: The paper details a specific protocol for quantum tomography and entanglement detection using dileptonic $t\bar{t}$ events, proposing the measurement of the parameter $D$ as a sufficient condition for entanglement ( $D < -1/3$ ).

Results

Theoretical Predictions: The analysis shows that $t\bar{t}$ $t \overset{ˉ}{t}$ pairs are entangled in the bulk of the phase space.
- In $q\bar{q}$ annihilation, the state is maximally entangled (a Bell state) in the ultrarelativistic limit ( $\beta \to 1$ ) and near the beam axis.
- In $gg$ fusion, entanglement is found in two regions: near the production threshold (where the pair forms a spin singlet) and at high transverse momentum (where it forms a spin triplet).
- For realistic LHC conditions (Run 2, $\sqrt{s} = 13$ TeV), the $gg$ channel dominates, and the overall concurrence reflects the $gg$ behavior, showing significant entanglement near the threshold.
Experimental Verification: The paper reports that the experimental proposal was implemented by the ATLAS and CMS collaborations using LHC Run 2 data.
- ATLAS measured $D = -0.537 \pm 0.019$ .
- CMS measured $D = -0.452^{+0.025}_{-0.026}$ .
- Both results satisfy the condition $D < -1/3$ , confirming the presence of entanglement with a statistical significance exceeding 5 standard deviations ( $5\sigma$ ). These constitute the highest-energy observations of entanglement to date.

Significance and Impact
The paper claims that its work has effectively spawned a new, rich field of QI in HEP (QIHEP). Its significance is threefold:

Theoretical: It offers a neat framework for applying QI tools to high-energy dynamics.
Phenomenological: It demonstrates that quantum tomography is a viable tool for probing high-energy physics, enabling the evaluation of all QI magnitudes from experimental data.
Experimental: It successfully identified the top quark as a platform for observing relativistic entanglement, leading to the first high-energy confirmation of quantum entanglement.

The authors note that their work has catalyzed further research, including studies on quantum discord, steering, Bell nonlocality, and "magic" in top quark production, as well as the extension of these concepts to other particles (bottom quarks, tau leptons, W/Z bosons) and applications in New Physics searches. The paper positions itself as a foundational step that has allowed for a continuous conceptual flow between condensed matter, quantum optics, and particle physics.

Technical Summary: Quantum Information in High-Energy Physics: a top subject

More like this