) 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}_{\mathrm{lab}}=100

MeV, cases of strongly entangled Bell-type states with only a small admixture of entanglement-spoiling contributions.

DOI: 10.1103/wr8m-4l77

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We investigate polarization states of the outgoing neutron-proton (

np

np

{E}_{\mathrm{lab}}=100

MeV, cases of strongly entangled Bell-type states with only a small admixture of entanglement-spoiling contributions.

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.

\frac{1}{2}

target, entanglement cannot be generated in unpolarized Compton scattering if the scattering amplitudes are real. We then consider polarized Compton scattering off the electron, the proton and the neutron. At low energy, we uncover a rich variety of maximally entangled Bell states and their unitary equivalents realized across different regions of the kinematic plane. Interestingly, the proton and neutron targets exhibit distinct patterns of entanglement. In the neutron case, the electric and magnetic polarizabilities dramatically influence the pattern and even the existence of entanglement. This suggests that entanglement can serve as a novel tool for investigating the detailed electromagnetic properties of the nucleons.

Quantum information in neutron-proton scattering from the

M

matrix

We study quantum-information aspects of neutron--proton scattering in the spin-space

M

-matrix framework. Four representative classes of input states are considered, namely diagonal mixed states, separable pure states, general two-qubit pure states, and a special Schmidt-like entangled subclass. For each class, ensemble-averaged output mutual information, reduced-state linear entropy, negativity, and geometric quantum discord are calculated in the relative momentum-- scattering angle plane. The results show that the outgoing spin correlations are governed jointly by scattering kinematics and by the structure of the incoming quantum ensemble. Input states with stronger intrinsic coherence or entanglement give larger maxima and higher minima in the mutual information, negativity, and geometric quantum discord. The enhanced regions of the mutual information and geometric discord depend on the input states, while the negativity maximum remains concentrated in the high-momentum backward-scattering region. These results extend earlier studies based on product-state entanglement power and provide an ensemble-based description of how spin correlations in neutron--proton scattering arise from the interplay between input-state structure and scattering dynamics.