Entanglement and non-separability of momenta and coordinates at colliders

We explore the possibility of testing in collider experiments whether phase-space variables are separable. We first study phase-space non-separability by means of EPR-like correlations. The original EPR setting is realized in an actual experiment, specifically in terms of coordinates and momenta, as per the original formulation, rather than spins or polarizations. We then show how to quantify the entanglement in the momenta of particle pairs by reducing the continuous variables to a two-qubit system through hemispherical projections. We discuss in detail the production of $\tau$-leptons at an electron collider, reconstructing the momenta of the former from their decays into pions and neutrinos, and demonstrate through a Monte Carlo simulation that phase-space non-separability can be experimentally assessed.