We discuss entanglement and the violation of the Collins-Gisin-Linden-Massar-Popescu (CGLMP) inequality in a system of two vector bosons produced in the decay of a spin-0 particle. We assume the most general CPT conserving, Lorentz- invariant coupling of the spin-0 particle with the daughter bosons. We compute the most general two-boson density matrix obtained by averaging over kinematical configurations with an appropriate probability distribution (which can be obtained when both bosons subsequently decay into fermion-antifermion). We show that the two-boson state is entangled and violates the CGLMP inequality for all values of the (anomalous) coupling constants and that in this case the state is entangled iff it can violate the CGLMP inequality. As an exemplary process of this kind we use the decay [Formula: see text] with anomalous coupling.
Higgs boson decays produce pairs of W bosons in a maximally entangled state, the spins of which can be expected to violate Bell inequalities. We show that the spin density matrix of the W± pair may be reconstructed experimentally from the directions of the charged lepton decay products, and from it the expectation values of various Bell operators determined. Numerical simulations of H→WW⁎ decays indicate that violation of a generalised CHSH inequality is unlikely to be measurable, however the CGLMP inequality is near-maximally violated. Experimental Bell tests could be performed at a variety of colliders and in different production channels. If reconstruction effects and backgrounds can be controlled then statistically significant violations could be observable even with datasets comparable to those already collected at the LHC.
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 explore the potential to study quantum entanglement through Bell-type inequalities in Higgs boson decays at a future muon collider. Our analysis focuses on the channel
μ+μ−→ννˉh→ννˉZZ∗, with one
Z decaying to charged leptons and the other decaying hadronically into jets. We study the violation of the CGLMP inequality using the optimal Bell operator for the bipartite qutrit system from
h→ZZ∗. The entanglement measure
I3 is constructed from spin-correlated angular observables of the
Z decay products. An unfolding method on the angular variables is applied to correct for hadronization and detector effects, recovering the advantage of the hadronic mode with higher event yield and reduced uncertainty. The study is performed at 1, 3, and 10 TeV centre-of-mass energies, assuming 10 ab
−1 integrated luminosity for each case. At 1 TeV, we use a boosted decision tree for signal isolation, while at higher energies, simple cut-based analyses are sufficient. We find clear Bell inequality violation with the expected values
I3=2.625±0.012,
2.623±0.004, and
2.582±0.010 for the 1, 3, and 10 TeV machines, respectively. Overall, a strong level of entanglement close to the maximum achievable value of 2.9149 for a two-qutrit system can be measured with very small uncertainties due to the large event yield in the hadronic mode.
We discuss quantum entanglement and violation of Bell inequalities in the $H\ensuremath{\rightarrow}ZZ$ decay, in particular when the two
Z-bosons decay into light leptons. Although such process implies an important suppression of the statistics, this is traded by clean signals from a ``quasi maximally entangled'' system, which makes it very promising to check these crucial phenomena at high energy. In this paper we devise a novel framework to extract from $H\ensuremath{\rightarrow}ZZ$ data all significant information related to this goal, in particular spin correlation observables. In this context we derive sufficient and necessary conditions for entanglement in terms of only two parameters. Likewise, we obtain a sufficient and improved condition for the violation of Bell-type inequalities. The numerical analysis shows that with a luminosity of $L=300\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ entanglement can be probed at $>3\ensuremath{\sigma}$ level. For $L=3\text{ }\text{ }{\mathrm{ab}}^{\ensuremath{-}1}$ (HL-LHC) entanglement can be probed beyond the $5\ensuremath{\sigma}$ level, while the sensitivity to a violation of the Bell inequalities is at the $4.5\ensuremath{\sigma}$ level.
We study quantum entanglement and test violation of Bell-type inequality at the Circular Electron Positron Collider (CEPC), which is one of the most attractive future collides. It is a promising particle collider designed to search new physics, make Standard Model (SM) precision measurements, and serving as a Higgs factory. Our study is based on a fast simulation of the Z boson pair production from Higgs boson decay at s = 250 GeV . The detector effects are also included in the simulation. The spin density matrix of the joint Z Z system is parametrized using irreducible tensor operators and reconstructed from the spherical coordinates of the decay leptons. To test Bell inequalities, we construct observable quantities for the H → Z Z * process in CEPC by using the Collins-Gisin-Linden-Massar-Popescu (CGLMP) inequality, whose value is determined from the density matrix of the Z boson pairs. The sensitivity of the Bell inequality violation is observed with more than 1 σ and the presence of the quantum entanglement is probed with more than 2 σ confidence level.