Tripartite entanglement from experimental data: $B^0\to K^{*0}\mu^+\mu^-$ as a case study

Abstract

We develop an angular analysis based on the reconstruction of the helicity amplitudes from dedicated experimental data corresponding to the tripartite state composed by one qutrit and two qubits, which arises in the three-body decays of a spin zero particle into one vector and a fermion pair. Starting from the associated spin density matrix of the final state, entanglement quantifiers were investigated and the corresponding significances were determined up to second order in the error propagation of the uncertainties of the angular measurements. As an application of our analysis, we performed a full quantum tomography of the final state in the $B^0\to K^{*0}\mu^+\mu^-$ decays using data recorded by LHCb collaboration. We found the presence of genuine quantum entanglement of the final state and also in both kaon-muon and di-muon subsystems. In recent years, $B$ meson decays received significant attention from both experimental and theoretical sides, and the proposed observables provide novel perspectives for studying them. Furthermore, this analysis could be also applied to other several processes if the complete experimental data were available for the helicity amplitudes reconstruction.