Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2310.10838 · Physical review. D/Physical review. D.

Quantum tomography of helicity states for general scattering processes

Alexander Bernal

Published Jun 10, 2024• 16 citations
arXivHTMLPDF

Abstract

Quantum tomography has become an indispensable tool in order to compute the density matrix ρ of quantum systems in physics. Recently, it has further gained importance as a basic step to test entanglement and violation of Bell inequalities in high-energy particle physics. In this work, we present the theoretical framework for reconstructing the helicity quantum initial state of a general scattering process. In particular, we perform an expansion of ρ over the irreducible tensor operators { T M L } and compute the corresponding coefficients uniquely by averaging, under properly chosen Wigner D-matrices weights, the angular distribution data of the final particles. Besides, we provide the explicit angular dependence of a novel generalization of the production matrix Γ and of the normalized differential cross section of the scattering. Finally, we rederive all our previous results from a quantum-information perspective using the Weyl-Wigner-Moyal formalism and we obtain, in addition, simple analytical expressions for the Wigner P and Q symbols. Published by the American Physical Society 2024

DOI
10.1103/physrevd.109.116007

Related papers

Quantum tomography for collider physics: illustrations with lepton-pair production

John C. Martens, John P. Ralston, J. D. Tapia Takaki

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 $$\chi ^{2}$$ 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.

arXiv:1707.01638•The European Physical Journal C•Dec 30, 2017•28 citations

Quantum orientation entanglement analysis of the interpolating helicity states between the instant form dynamics and the light-front dynamics

Deepasika Dayananda, Chueng-Ryong Ji

The interplay between quantum orientation entanglement and Wigner rotation plays a fundamental role in understanding the behavior of spin angular momentum in quantum states. To analyze the quantum orientation entanglement of the relativistic helicity states interpolating between the Jacob-Wick helicity and the light-front helicity, we examine the relative angle between the particle's momentum direction and the spin orientation for the interpolating helicity states. For this analysis, we introduce a novel method for expanding the interpolating helicity states in terms of the Jacob-Wick helicity. The corresponding probabilistic coefficients follow the structure of the Wigner d-matrix elements, which we use for the interpretation of the quantum orientation entanglement manifested in the angular distributions of the interpolating scattering helicity amplitudes. As an explicit demonstration, we compute the interpolating helicity amplitudes for the pair production of spin-1 (vector) particles in the annihilation of two spin-0 (scalar) particles, focusing primarily on their contact interaction. In particular, we identify the critical interpolation angle that bifurcates the dynamical branches between the instant-form dynamics and the light-front dynamics and discuss the underlying orientation entanglement in the interpolating helicity amplitudes.

hep-thCross-listedarXiv:2603.18208•Mar 20, 2026

Wigner tomography of multispin quantum states

David Leiner, Robert Zeier, Steffen J. Glaser

We study the tomography of multispin quantum states in the context of finite-dimensional Wigner representations. An arbitrary operator can be completely characterized and visualized using multiple shapes assembled from linear combinations of spherical harmonics [A. Garon, R. Zeier, and S. J. Glaser, Phys. Rev. A 91, 042122 (2015)]. We develop a general methodology to experimentally recover these shapes by measuring expectation values of rotated axial spherical tensor operators and provide an interpretation in terms of fictitious multipole potentials. Our approach is experimentally demonstrated for quantum systems consisting of up to three spins using nuclear magnetic resonance spectroscopy.

arXiv:1707.08465•Physical Review A•Dec 18, 2017•41 citations

Regularized entanglement entropy of electron-positron scattering with a witness photon

Shanmuka Shivashankara, Grace Gogliettino

Regularized quantum information metrics are calculated for the scattering process e − e + → γ , Z → μ − μ + that has a witness photon entangled with the initial electron-positron state. Unitarity implies the correct regularization of divergences that appear in both the final density matrix and von Neumann entanglement entropies. The entropies are found to quantify uncertainty or randomness. The variation of information, entanglement entropy, and correlation between the muon’s and witness photon’s helicities are found to convey equivalent information. The magnitude of the muon’s expected helicity rises (falls) as the helicity entropy falls (rises). Area, or the scattering cross section, is a source of entropy for the muon’s helicity entropy and momentum entropy. The muon’s differential angular entropy distribution is similar to the differential angular cross section distribution, capturing the forward-backward asymmetry at high center-of-mass energies. Published by the American Physical Society 2024

arXiv:2405.11799•Physical review. D/Physical review. D.•Nov 4, 2024•5 citations

Searching Quantum Entanglement in $p\ p\to Z\ Z$ process

Alim Ruzi, Youpeng Wu, Ran Ding +1 more

Recent studies have shown that observing entangled particle states at a particle collider like Large Hadron Collider (LHC) and testing violation of Bell inequality in them can open up new research area for high energy physics study. We examine the presence of quantum entanglement in the $pp\to ZZ\to 4\ell$ process at leading order. We apply generally recognized method, quantum state tomography, to reconstruct spin density matrix of the joint $ZZ$ system, through which all the relevant observables can be obtained. The angular distribution of the final leptons are obtained from simulated events using Monte-Carlo program, which is used to reconstruct spin density matrix. Non-zero value of the lower bound of the concurrence is measured with simulated data. The numerical analysis shows that with the luminosity corresponding to LHC Run 2+3, entanglement can be probed at $2 σ$ level and up to 3.75$σ$ level for High-Luminosity LHC data ($3 \rm{ab}^{-1}$), revealing the possibility of finding quantum entanglement in real collider experiment.

arXiv:2506.16077•Jun 19, 2025•0 citations

Wigner process tomography: Visualization of spin propagators and their spinor properties

David Leiner, Steffen J. Glaser

We study the tomography of propagators for spin systems in the context of finite-dimensional Wigner representations, which completely characterize and visualize operators using shapes assembled from linear combinations of spherical harmonics. The Wigner representation of a propagator can be experimentally recovered by measuring expectation values of rotated axial spherical tensor operators in an augmented system with an additional ancilla qubit. The methodology is experimentally demonstrated for standard one-qubit quantum gates using nuclear magnetic resonance spectroscopy. In particular, this approach provides a direct and compelling visualization of the spinor property of the propagators corresponding to the rotation of a spin-1/2 particle.

arXiv:1803.11053•Physical Review A•Jul 10, 2018•30 citations
Quantum tomography has become an indispensable tool in order to compute the density matrix ρ of quantum systems in physics. Recently, it has further gained importance as a basic step to test entanglement and violation of Bell inequalities in high-energy particle physics. In this work, we present the theoretical framework for reconstructing the helicity quantum initial state of a general scattering process. In particular, we perform an expansion of ρ over the irreducible tensor operators { T M L } and compute the corresponding coefficients uniquely by averaging, under properly chosen Wigner D-matrices weights, the angular distribution data of the final particles. Besides, we provide the explicit angular dependence of a novel generalization of the production matrix Γ and of the normalized differential cross section of the scattering. Finally, we rederive all our previous results from a quantum-information perspective using the Weyl-Wigner-Moyal formalism and we obtain, in addition, simple analytical expressions for the Wigner P and Q symbols. Published by the American Physical Society 2024
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.
The interplay between quantum orientation entanglement and Wigner rotation plays a fundamental role in understanding the behavior of spin angular momentum in quantum states. To analyze the quantum orientation entanglement of the relativistic helicity states interpolating between the Jacob-Wick helicity and the light-front helicity, we examine the relative angle between the particle's momentum direction and the spin orientation for the interpolating helicity states. For this analysis, we introduce a novel method for expanding the interpolating helicity states in terms of the Jacob-Wick helicity. The corresponding probabilistic coefficients follow the structure of the Wigner d-matrix elements, which we use for the interpretation of the quantum orientation entanglement manifested in the angular distributions of the interpolating scattering helicity amplitudes. As an explicit demonstration, we compute the interpolating helicity amplitudes for the pair production of spin-1 (vector) particles in the annihilation of two spin-0 (scalar) particles, focusing primarily on their contact interaction. In particular, we identify the critical interpolation angle that bifurcates the dynamical branches between the instant-form dynamics and the light-front dynamics and discuss the underlying orientation entanglement in the interpolating helicity amplitudes.
We study the tomography of multispin quantum states in the context of finite-dimensional Wigner representations. An arbitrary operator can be completely characterized and visualized using multiple shapes assembled from linear combinations of spherical harmonics [A. Garon, R. Zeier, and S. J. Glaser, Phys. Rev. A 91, 042122 (2015)]. We develop a general methodology to experimentally recover these shapes by measuring expectation values of rotated axial spherical tensor operators and provide an interpretation in terms of fictitious multipole potentials. Our approach is experimentally demonstrated for quantum systems consisting of up to three spins using nuclear magnetic resonance spectroscopy.
Regularized quantum information metrics are calculated for the scattering process e − e + → γ , Z → μ − μ + that has a witness photon entangled with the initial electron-positron state. Unitarity implies the correct regularization of divergences that appear in both the final density matrix and von Neumann entanglement entropies. The entropies are found to quantify uncertainty or randomness. The variation of information, entanglement entropy, and correlation between the muon’s and witness photon’s helicities are found to convey equivalent information. The magnitude of the muon’s expected helicity rises (falls) as the helicity entropy falls (rises). Area, or the scattering cross section, is a source of entropy for the muon’s helicity entropy and momentum entropy. The muon’s differential angular entropy distribution is similar to the differential angular cross section distribution, capturing the forward-backward asymmetry at high center-of-mass energies. Published by the American Physical Society 2024
Searching Quantum Entanglement in p p→Z Zp\ p\to Z\ Zp p→Z Z process
Recent studies have shown that observing entangled particle states at a particle collider like Large Hadron Collider (LHC) and testing violation of Bell inequality in them can open up new research area for high energy physics study. We examine the presence of quantum entanglement in the pp→ZZ→4ℓpp\to ZZ\to 4\ellpp→ZZ→4ℓ process at leading order. We apply generally recognized method, quantum state tomography, to reconstruct spin density matrix of the joint ZZZZZZ system, through which all the relevant observables can be obtained. The angular distribution of the final leptons are obtained from simulated events using Monte-Carlo program, which is used to reconstruct spin density matrix. Non-zero value of the lower bound of the concurrence is measured with simulated data. The numerical analysis shows that with the luminosity corresponding to LHC Run 2+3, entanglement can be probed at 2σ2 σ2σ level and up to 3.75σσσ level for High-Luminosity LHC data (3ab−13 \rm{ab}^{-1}3ab−1), revealing the possibility of finding quantum entanglement in real collider experiment.
We study the tomography of propagators for spin systems in the context of finite-dimensional Wigner representations, which completely characterize and visualize operators using shapes assembled from linear combinations of spherical harmonics. The Wigner representation of a propagator can be experimentally recovered by measuring expectation values of rotated axial spherical tensor operators in an augmented system with an additional ancilla qubit. The methodology is experimentally demonstrated for standard one-qubit quantum gates using nuclear magnetic resonance spectroscopy. In particular, this approach provides a direct and compelling visualization of the spinor property of the propagators corresponding to the rotation of a spin-1/2 particle.