Abstract This paper provides explicit and detailed quantum field theory (QFT) computations of polarizations correlations of emerging particles in several processes in QED, Electroweak Theory, and even in particle productions from strings, and hence are based on dynamical theries. The novel properties observed in the computations of such polarizations correlations, as predicted by QFT, is that they depend on the speed of the colliding particles, and, in some cases, even on coupling parameters ratios as well as on mass ratios of the underlying theory. These investigations clearly show that arguments based simply on combining spins to generate probabilities of such polarization correlations are not reliable. The novel properties obtained, with details of derivations provided here, hopefully would call for experiments on polarizations correlations which would monitor speeds of colliding particles, and, would, in turn, lead to new tests of the fundamental interactions of QFT such as of QED and of the Electroweak Theory.
Spin correlations of e + e − pair productions of two colliding photons are investigated and explicit expressions for their corresponding probabilities are derived and found to be energy (speed) dependent, for initially linearly and circularly polarized photons, different from those obtained by simply combining the spins of the relevant particles, for initially polarized photons. These expressions also depend on the angles of spin of e + (and/or of e −), for initially linearly polarized photons, but not for circularly polarized photons, as a function of the energy. It is remarkable that these explicit results obtained from quantum field theory show a clear violation of Bell's inequality of Local Hidden Variables theories at all energies beyond that of the threshold one for particle production, in support of quantum field theory in the relativistic regime. We hope that our explicit expression will lead to experiments, of the type described in the bulk of this paper, which can monitor energy (and speed) in polarization correlation experiments.
We systematically study the spin correlations and quantum entanglement in transversely polarized electron-positron collisions. We find that the
s-channel QED process
e−e+→ffˉ produces a maximally entangled state in the entire phase space when the initial beams are transversely polarized, while the quantum magic varies in different phase space points for the maximally entangled Bell states. For electroweak processes, the spin configuration of final states depends on chiral couplings, and the entanglement is also greatly enhanced by transverse polarization as in the QED process. For Bhabha scattering with additional
t-channel contributions, the transverse polarization still increases the final state entanglement, although with some dilution. The sensitive dependence of final spin states on the transverse polarization makes the beam polarization a powerful tool for generating and controlling quantum entanglement in collider experiments, opening up new opportunities for quantum information studies at high-energy colliders.
We explore the phenomenology of quantum entanglement at collider experiments by computing the polarization density matrix of processes yielding two massive gauge bosons. After reviewing the formalism, we detail observables suitable to test the presence of entanglement and quantum correlations in the di-boson system. The implied violation of Bell inequalities can be observed with future data at the LHC in the decays of the Higgs boson to
Z boson pairs.
Abstract Quantum entanglement of weak interaction gauge bosons produced at colliders can be explored by computing the corresponding polarization density matrix. To this end, we consider the Higgs boson decays
H→WW∗ H → W W ∗ and
H→ZZ∗ H → Z Z ∗ , in which
W∗ W ∗ and
Z∗ Z ∗ are off-shell states, and the WW , WZ and ZZ di-boson production in proton collisions. The polarization density matrix of the di-boson state is determined by the amplitude of the production process and can be experimentally reconstructed from the angular distribution of the momenta of the final states into which the gauge bosons decay. We show that a suitable instance of the Bell inequality is violated in
H→ZZ∗ H → Z Z ∗ to a degree that can be tested at the LHC with future data. The same Bell inequality is violated in the production of WW and ZZ boson pairs for invariant masses above 900 GeV and scattering angles close to
π/2 π / 2 in the center of mass frame. LHC data in this case are not sufficient to establish the violation of the Bell inequality. We also analyze the prospects for detecting Bell inequality violations in di-boson final states at future
e+e− e + e - and muon colliders. A further observable that provides a lower bound on the amount of polarization entanglement in the di-boson system is computed for each of the examined processes. The analytic expressions for the polarization density matrices are presented in full in an Appendix. We also provide the unitary matrices required in the optimization procedure necessary in testing the Bell inequalities.
We propose a new formalism for quantum entanglement (QE), and study its generic searches at the colliders. For a general quantum system with
N particles, we show that the quantum space (the total spin polarization parameter space) is complex projective space, and the classical space (the spin polarization parameter space for classical theory) is the cartesian product of the complex projective spaces. Thus, the quantum entanglement space is the difference of these two spaces. For the
ff,
AA,
Af,
fff, and
ffA systems, we propose their discriminants
Δi. The corresponding classical spaces are the discriminant locus
Δ=0 for
ff system, and intersections of the discriminant loci
Δi=0 for
AA,
Af,
fff, and
ffA systems in the quantum space. In particular, for two fermion
ff system, we prove that our discriminant criterion is equivalent to the original Peres-Horodecki criterion and the CHSH criterion. And thus our quantum entanglement space is indeed Bell non-local. With the collider searches, we can reconstruct the discriminants from various measurements, and probe the quantum entanglement spaces via a fundamental approach at exact level. In addition, for the specific approach, we present a comprehensive framework to detect quantum entanglement in high-energy multi-particle systems, spanning fermion pairs (
ttˉ,
τ+τ−), bosonic pairs (
W−W+), and hybrid or three-body systems (
W−t,
ttt,
ttˉW−), by diverse observables through angular correlations in decay products. These results establish model-independent methodologies for probing QE across collider experiments, bridging quantum information principles with high-energy phenomenology, while offering novel pathways to explore exotic particles and quantum properties in multi-particle systems.
Abstract Quantum entanglement and Bell nonlocality—cornerstones of quantum mechanics—have traditionally been investigated only in low-energy experimental settings. Only recently, these fundamental phenomena have come to be explored in the high-energy domain of particle physics, where collider experiments offer a powerful new platform for studying the phenomenology of quantum correlations. We present here recent results on the detection of entanglement and Bell nonlocality in processes such as tau–lepton, WW , and ZZ pair production, illustrating the potential of future lepton colliders to probe the quantum properties of fundamental interactions.