Searching for entanglement in final polarization states of the neutron-proton scattering

TL;DR

This paper investigates the polarization states of neutron-proton scattering to identify entanglement, calculating spin correlations and polarizations using a high-precision potential, revealing entanglement properties at various energies.

Contribution

It provides a comprehensive calculation of final spin states and correlations, including contributions from various polarization transfers, and identifies conditions leading to entangled states.

Findings

Final states are mostly mixed, with pure states occurring at maximal initial polarizations.

Entanglement increases with energy, especially in pure states from highly polarized initial nucleons.

At 100 MeV, strongly entangled Bell-type states are observed with minimal entanglement-spoiling effects.

Abstract

We investigate polarization states of the outgoing neutron-proton ($np$) pair in elastic polarized neutron and proton scattering, aiming to find unambiguous evidence for entanglement of their spin states. To obtain complete information about these states, we calculate, using the high precision nucleon-nucleon potential AV18, the final polarizations of the neutron and proton as well as their spin correlation coefficients, which unequivocally define the corresponding spin density matrix. We compute all terms contributing to polarizations and spin correlations, e.g. not only induced polarizations and correlations resulting from unpolarized $np$ scattering, but also contributions from single polarization and correlation transfers from individual polarized incoming nucleons, and, for the first time, allotment to both quantities stemming from a doubly spin polarized initial state. We find that for the most part the final spin states are statistical mixture of states.The only pure states occur for highly polarized incoming neutrons and protons with maximal polarizations. By quantifying the degree of entanglement through entanglement power and concurrence, we observed that the entanglement of impure final states increases with energy. Among the pure spin states resulting from incoming states with maximal neutron and proton polarizations, we found, at $E_{lab}=100$~MeV, cases of strongly entangled Bell-type states with only a small admixture of entanglement-spoiling contributions.