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:2606.16365

Determining the Spin Density Matrix via Its Rank and Probing the Quantum Entanglement and Bell Non-Locality at the Lepton Colliders

Liwei Liu, X. Q. Hao, Dianwei Wang, Lina Wu, Tianjun Li

Published Jun 15, 2026• 0 citations
arXivHTMLPDF

Abstract

Considering two-fermion $F_a F_b$ productions and decays via one scalar or photon exchange at the $e^+e^-$ collider, we show that the rank $r_ρ$ of spin density matrix $ρ$ is equal to the number of degrees of freedom of the mediator. For one generic scalar exchange, the spin density matrix is rank one for a pure state. With rank-one condition, we can determine the spin analyzing powers for $F_a$ and $F_b$ and their product if the CP symmetry is violated and conserved, respectively, and probe the CP violation. These results can be applied to the $η_c \to Λ{\bar Λ}$ at the BESIII experiment and the Higgs $\to ττ$ at the LHC. For one photon exchange, the spin density matrix is rank two for a mixed state. Considering the $Λ\bar Λ$ productions and decays at the BESIII experiment as an example, we show that the spin analyzing powers for $F_a$ and $ F_b$ can be determined by the rank-two conditions in details. Therefore, we can reconstruct the spin density matrices, probe the quantum entanglement and Bell non-locality, and evade the no-go theorem. Furthermore, we conjecture that the $N\times N$ spin density matrix with $r_ρ \le N-2 $ can be reconstructed at the lepton colliders in general.

DOI
10.48550/arxiv.2606.16365

Related papers

Determining the Spin-Analyzing Powers via Invariants of the Spin Correlation Matrices and Probing the Bell Non-Locality at the Lepton Colliders

Dianwei Wang, X. Q. Hao, Liwei Liu +2 more

We consider the two-fermion $F_a F_b$ productions and decays via one mediator exchange at the $e^+e^-$ collider. With the assumption that the spin is defined via the Lorentz symmetry, or considering the implicit symmetry in the spin density matrix, we prove that the trace ${\rm Tr} [C]$ of the spin correlation matrix $C$ is an invariant quantity, and is invariant under basis rotations. Thus, for the exchanges of one mediator such as scalar and gauge boson, we can determine the product of the spin-analyzing powers for $F_a F_b$ via ${\rm Tr} [C]$, and reconstruct the spin correlation matrix. With the CHSH-Horodecki criterion, we can probe the Bell non-locality, and evade the no-go theorem. To be concrete, we study the Bell non-locality for the $Λ\bar Λ$ productions and decays at the BESIII experiment. In addition, the invariant ${\rm Tr} [C]$ is a new physics observable to probe the new physics beyond the Standard Model (SM) and study the SM precision measurements. Moreover, for the scalar exchanges, we discuss the general invariants of the spin correlation matrices and the related phenomenological consequences.

arXiv:2605.13250•May 13, 2026•0 citations

Searching quantum entanglement in the pp → ZZ process*

Alim Ruzi, Youpeng Wu, Ran 然 Ding 丁 +1 more

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

Chinese Physics C•Oct 15, 2025•3 citations

Quantum properties of heavy-fermion pairs at a lepton collider with polarised beams

Mohammad Mahdi Altakach, Priyanka Lamba, Fabio Maltoni +1 more

We investigate the quantum properties of heavy-fermion pairs, such as $t\bar t$ or $τ^+τ^-$, produced in lepton-lepton collisions with polarised beams. Focusing on spin correlations, entanglement, Bell-inequality violation, and quantum-information-theoretic measures such as purity and magic, we analyse how beam polarisation shapes the structure of the spin-density matrix. We derive analytic expressions for a wide range of helicity configurations, including both Standard Model contributions and generic new-physics effects parametrised by scalar, vector, and tensor four-fermion operators within an effective field theory framework. We show that beam polarisation unlocks a substantially richer set of spin configurations and significantly enhances sensitivity to non-standard interactions. As a phenomenological application, we study $t\bar t$ production at a future linear collider and demonstrate that quantum observables provide a comprehensive and complementary probe of top-quark interactions and stronger constraints on the scale of new physics.

hep-phCross-listedarXiv:2601.09558•Jan 15, 2026•0 citations

An improved Bell-CHSH observable for gauge boson pairs

R. P. Grabarczyk

For particles decaying without parity violation, it is impossible to reconstruct the full spin-density matrix from the velocities of their decay products. In this work, we consider Bell inequalities based on squares of spin operators. The corresponding Bell operators probe only the part of the density matrix that can be reconstructed from any gauge boson decay or splitting to fermions, which is accessible regardless of whether parity is violated. We find that our new choice of Bell operator has promising properties regarding states seen at colliders. In particular, it substantially outperforms the inequality previously used for the $pp \rightarrow ZZ$ process at the LHC in terms of the phase space volume in which it is violated. We also conduct the first investigation of Bell violation in a system involving gauge bosons mediating different interactions, namely the $W$ boson and gluon in the $pp \rightarrow W^{\pm} (g\rightarrow b\bar{b})$ process.

arXiv:2410.18022•Oct 23, 2024•1 citation

Testing Bell inequalities and probing quantum entanglement at a muon collider

Alim Ruzi, Youpeng Wu, Ran Ding +3 more

A bstract A muon collider represents a promising candidate for the next generation of particle physics experiments after the expected end of LHC operations in the early 2040s. Rare or hard-to-detect processes at the LHC, such as the production of multiple gauge bosons, become accessible at a TeV muon collider. We present here the prospects of detecting quantum entanglement and the violation of Bell inequalities in H → ZZ → 4 ℓ events at a potential future muon collider. We show that the spin density matrix of the Z boson pairs can be reconstructed using the kinematics of the charged leptons from the Z boson decays. Once the density matrix is determined, it is straightforward to obtain the expectation values of various Bell operators and test the quantum entanglement between the Z boson pair. Through a detailed study based on Monte-Carlo simulation, we show that the generalized CGLMP inequality can be maximally violated, and testing Bell inequalities could be established with high significance.

arXiv:2408.05429•Journal of High Energy Physics•Oct 29, 2024•17 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
Considering two-fermion FaFbF_a F_bFa​Fb​ productions and decays via one scalar or photon exchange at the e+e−e^+e^-e+e− collider, we show that the rank rρr_ρrρ​ of spin density matrix ρρρ is equal to the number of degrees of freedom of the mediator. For one generic scalar exchange, the spin density matrix is rank one for a pure state. With rank-one condition, we can determine the spin analyzing powers for FaF_aFa​ and FbF_bFb​ and their product if the CP symmetry is violated and conserved, respectively, and probe the CP violation. These results can be applied to the ηc→ΛΛˉη_c \to Λ{\bar Λ}ηc​→ΛΛˉ at the BESIII experiment and the Higgs →ττ\to ττ→ττ at the LHC. For one photon exchange, the spin density matrix is rank two for a mixed state. Considering the ΛΛˉΛ\bar ΛΛΛˉ productions and decays at the BESIII experiment as an example, we show that the spin analyzing powers for FaF_aFa​ and Fb F_bFb​ can be determined by the rank-two conditions in details. Therefore, we can reconstruct the spin density matrices, probe the quantum entanglement and Bell non-locality, and evade the no-go theorem. Furthermore, we conjecture that the N×NN\times NN×N spin density matrix with rρ≤N−2r_ρ \le N-2 rρ​≤N−2 can be reconstructed at the lepton colliders in general.
We consider the two-fermion FaFbF_a F_bFa​Fb​ productions and decays via one mediator exchange at the e+e−e^+e^-e+e− collider. With the assumption that the spin is defined via the Lorentz symmetry, or considering the implicit symmetry in the spin density matrix, we prove that the trace Tr[C]{\rm Tr} [C]Tr[C] of the spin correlation matrix CCC is an invariant quantity, and is invariant under basis rotations. Thus, for the exchanges of one mediator such as scalar and gauge boson, we can determine the product of the spin-analyzing powers for FaFbF_a F_bFa​Fb​ via Tr[C]{\rm Tr} [C]Tr[C], and reconstruct the spin correlation matrix. With the CHSH-Horodecki criterion, we can probe the Bell non-locality, and evade the no-go theorem. To be concrete, we study the Bell non-locality for the ΛΛˉΛ\bar ΛΛΛˉ productions and decays at the BESIII experiment. In addition, the invariant Tr[C]{\rm Tr} [C]Tr[C] is a new physics observable to probe the new physics beyond the Standard Model (SM) and study the SM precision measurements. Moreover, for the scalar exchanges, we discuss the general invariants of the spin correlation matrices and the related phenomenological consequences.
Abstract Recent studies have shown that observing entangled particle states at a particle collider, such as the Large Hadron Collider (LHC), and testing the violation of Bell inequality in them can open up new research areas for studying high energy physics. We examine the presence of quantum entanglement in the process at leading order. We apply a generally recognized method, quantum state tomography, to reconstruct the spin density matrix of the joint ZZ system, through which all the relevant observables can be obtained. The angular distribution of the final leptons is obtained from simulated events using a Monte-Carlo program, which is used to reconstruct the spin density matrix. A non-zero value of the lower bound of the concurrence is measured with the simulated data. The numerical analysis shows that, with the luminosity corresponding to LHC Run 2+3, entanglement can be probed at the 2 level and up to the 3.75 level for High-Luminosity LHC data (3ab -1 ), revealing the possibility of finding quantum entanglement in real collider experiments.
We investigate the quantum properties of heavy-fermion pairs, such as ttˉt\bar tttˉ or τ+τ−τ^+τ^-τ+τ−, produced in lepton-lepton collisions with polarised beams. Focusing on spin correlations, entanglement, Bell-inequality violation, and quantum-information-theoretic measures such as purity and magic, we analyse how beam polarisation shapes the structure of the spin-density matrix. We derive analytic expressions for a wide range of helicity configurations, including both Standard Model contributions and generic new-physics effects parametrised by scalar, vector, and tensor four-fermion operators within an effective field theory framework. We show that beam polarisation unlocks a substantially richer set of spin configurations and significantly enhances sensitivity to non-standard interactions. As a phenomenological application, we study ttˉt\bar tttˉ production at a future linear collider and demonstrate that quantum observables provide a comprehensive and complementary probe of top-quark interactions and stronger constraints on the scale of new physics.
For particles decaying without parity violation, it is impossible to reconstruct the full spin-density matrix from the velocities of their decay products. In this work, we consider Bell inequalities based on squares of spin operators. The corresponding Bell operators probe only the part of the density matrix that can be reconstructed from any gauge boson decay or splitting to fermions, which is accessible regardless of whether parity is violated. We find that our new choice of Bell operator has promising properties regarding states seen at colliders. In particular, it substantially outperforms the inequality previously used for the pp→ZZpp \rightarrow ZZpp→ZZ process at the LHC in terms of the phase space volume in which it is violated. We also conduct the first investigation of Bell violation in a system involving gauge bosons mediating different interactions, namely the WWW boson and gluon in the pp→W±(g→bbˉ)pp \rightarrow W^{\pm} (g\rightarrow b\bar{b})pp→W±(g→bbˉ) process.
A bstract A muon collider represents a promising candidate for the next generation of particle physics experiments after the expected end of LHC operations in the early 2040s. Rare or hard-to-detect processes at the LHC, such as the production of multiple gauge bosons, become accessible at a TeV muon collider. We present here the prospects of detecting quantum entanglement and the violation of Bell inequalities in H → ZZ → 4 ℓ events at a potential future muon collider. We show that the spin density matrix of the Z boson pairs can be reconstructed using the kinematics of the charged leptons from the Z boson decays. Once the density matrix is determined, it is straightforward to obtain the expectation values of various Bell operators and test the quantum entanglement between the Z boson pair. Through a detailed study based on Monte-Carlo simulation, we show that the generalized CGLMP inequality can be maximally violated, and testing Bell inequalities could be established with high significance.
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.