Scattering in quantum field theory produces a superposition of outcomes — elastic reflection, particle production, bound state formation — all entangled in the final wavefunction. Extracting the probability of each channel requires projecting onto the appropriate asymptotic state. In real experiments, detectors perform this projection. In simulations, you have the full wavefunction but need to decompose it.
The paper uses entanglement structure to do the decomposition. After the collision, the late-time wavefunction is represented as a Matrix Product State (MPS). A Schmidt decomposition at a spatial bipartition — cutting the lattice between the left-moving and right-moving products — reveals the entanglement spectrum. Each Schmidt value corresponds to a scattering channel, and its square gives the channel's probability.
The method is experimentally inspired: it mirrors what a particle detector does, which is to identify particles by their spatial separation from the collision point. In the MPS, spatial separation corresponds to bipartition position, and the entanglement across the cut encodes the correlation between left-going and right-going particles.
Demonstrated on the Ising field theory in 1+1 dimensions, where meson-meson collisions produce elastic and inelastic channels. The method deterministically identifies outgoing particle types — not statistically (by sampling) but exactly (by reading the entanglement spectrum). Heavy particles in the inelastic channel appear as specific Schmidt vectors with distinctive spatial profiles.
The entanglement structure of the wavefunction is the experimental data of the simulation. You don't need to add a detector — the entanglement is the detector.