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Journal of the Physical Society of Japan

Concurrence in Neutron–Proton Scattering for Polarization-Induced Mixed States

Hina Matsufuji, Hiroki Nishibata, Hideyuki SAKAI, T. Wakasa

Published Aug 6, 2026• 0 citations
Publisher

Abstract

We investigate spin entanglement generated in neutron–proton scattering by evaluating the concurrence from the scattered two-nucleon density matrix. While previous studies mainly discussed pure initial spin states, the present work extends the analysis to polarization-induced mixed states, including partially polarized and unpolarized cases, within a unified framework. Initial polarization directions along the x, y, and [Formula: see text] axes are considered. Here, the [Formula: see text] axis is along the incident momentum, the y axis is normal to the scattering plane, and the x axis completes a right-handed system. We then examine the dependence of the concurrence on the incident energy, scattering angle, polarization degree, and polarization direction. The results show that the angular dependence of the concurrence becomes more pronounced as the incident energy increases. Although the concurrence tends to decrease overall as the polarization degree is reduced, this behavior is not uniform over all scattering angles, and in some regions unpolarized mixed states yield larger concurrence than fully polarized pure states. The concurrence is also found to be sensitive to the initial polarization direction. These features indicate that the entanglement generated in neutron–proton scattering reflects the interference structure of the scattering amplitudes. The present framework provides a basis for discussing spin entanglement under more realistic experimental conditions beyond pure-state idealizations.

DOI
10.7566/jpsj.95.094201

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We investigate spin entanglement generated in neutron–proton scattering by evaluating the concurrence from the scattered two-nucleon density matrix. While previous studies mainly discussed pure initial spin states, the present work extends the analysis to polarization-induced mixed states, including partially polarized and unpolarized cases, within a unified framework. Initial polarization directions along the x, y, and [Formula: see text] axes are considered. Here, the [Formula: see text] axis is along the incident momentum, the y axis is normal to the scattering plane, and the x axis completes a right-handed system. We then examine the dependence of the concurrence on the incident energy, scattering angle, polarization degree, and polarization direction. The results show that the angular dependence of the concurrence becomes more pronounced as the incident energy increases. Although the concurrence tends to decrease overall as the polarization degree is reduced, this behavior is not uniform over all scattering angles, and in some regions unpolarized mixed states yield larger concurrence than fully polarized pure states. The concurrence is also found to be sensitive to the initial polarization direction. These features indicate that the entanglement generated in neutron–proton scattering reflects the interference structure of the scattering amplitudes. The present framework provides a basis for discussing spin entanglement under more realistic experimental conditions beyond pure-state idealizations.
We investigate polarization states of the outgoing neutron-proton (npnpnp) 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 npnpnp 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 Elab=100{E}_{\mathrm{lab}}=100Elab​=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 (npnpnp) 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 npnpnp 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 Elab=100E_{lab}=100Elab​=100~MeV, cases of strongly entangled Bell-type states with only a small admixture of entanglement-spoiling contributions.
Quantum information in neutron-proton scattering from the MMM matrix
We study quantum-information aspects of neutron--proton scattering in the spin-space MMM-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.
In this Letter, I work out spin entanglement properties of neutron-proton scattering using the exact S-matrix, considering both S-wave and higher partial wave contributions. The dependence of spin entanglement on momentum, scattering angle, and initial spin configuration is investigated for realistic nuclear forces, while low-energy properties of spin entanglement are analyzed within the framework of pionless effective field theory at leading order. New connections are found between spin entanglement and symmetry emergence of strong interactions. These results lead to a more complete understanding of how spin entanglement is generated via neutron-proton interaction. They also lay the theoretical foundation for controllable production of entangled nucleon-nucleon pairs in future experiments.
We study spin-spin entanglement in the final state photon-nucleon system in Compton scattering, both at low energy below the pion threshold and at high energy in perturbative QCD to next-to-leading order. We first establish a no-go theorem showing that, for any spin-12\frac{1}{2}21​ 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.
Several recent experiments on liquid and solid samples containing protons or deuterons show an interesting anomaly, which is a shortfall in the intensity of energetic neutrons scattered by the samples. Previously we demonstrated that quantum correlations in the spatial and spin degrees of freedom of the hydrogen isotopes lead to entanglement in scattering and a reduction in the scattered intensity. The viability of short-lived quantum correlations as the cause of the observed anomalies is further explored and found to be entirely feasible. General features of the basic premiss, that quantum entanglement reduces the scattered signal, are discussed and the interpretation of the neutron scattering experiments is set in context to related work on other systems. For the experiments in question, the duration of a scattering event, τ s , is a fraction of a femtosecond which is extremely short compared to solid-state relaxation times. Increasing τ s , by suitably changing experimental conditions, restores the intensity to the standard value calculated from the single atom cross-section and concentration of particles. Our physical picture of the restoration is evolution with increasing τ s from a pure state of the particles (described by a wavefunction) to a mixed state (described by a density matrix) that is created, through decoherence, by steadily engaging the solid-state environment of the particles.