Measurement of Bell-type inequalities and quantum entanglement from $\Lambda$-hyperon spin correlations at high energy colliders

Spin correlations of $\Lambda$-hyperons embedded in the QCD strings formed in high energy collider experiments provide unique insight into their locality and entanglement features. We show from general considerations that while the Clauser-Horne-Shimony-Holt inequality is less stringent for such states, they provide a benchmark for quantum-to-classical transitions induced by varying i) the associated hadron multiplicity, ii) the spin of nucleons, iii) the separation in rapidity between pairs, and iv) the kinematic regimes accessed. These studies also enable the extraction of quantitative measures of quantum entanglement. We first explore such questions within a simple model of a QCD string composed of singlets of two partial distinguishable fermion flavors and compare analytical results to those obtained on quantum hardware. We further discuss a class of spin Hamiltonians that model the dynamics of $\Lambda$ spin correlations. Prospects for extracting quantum features of QCD strings from hyperon measurements at current and future colliders are outlined.