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Physical Review C

Quantum information in nucleon-nucleon scattering

Dong Bai

Published Apr 21, 2023• 13 citations
Publisher

Abstract

Nucleon-nucleon scattering is a fundamental process in low-energy nuclear physics. Although its spin correlations have been studied intensively, few works take the perspective of quantum information science. In this work, I explore the quantum information aspects of spin correlations in the partially polarized neutron-proton scattering in the $S$ wave. It is found that the spin mutual information, entanglement and discord of the out-states, when averaged over the possible in-states, all vary in a similar way with respect to the relative momentum. The novel connection between emergent symmetry and spin entanglement found by a previous study [Phys. Rev. Lett. 122, 102001 (2019)] could then be extended naturally to spin correlations beyond entanglement.

DOI
10.1103/physrevc.107.044005

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Nucleon-nucleon scattering is a fundamental process in low-energy nuclear physics. Although its spin correlations have been studied intensively, few works take the perspective of quantum information science. In this work, I explore the quantum information aspects of spin correlations in the partially polarized neutron-proton scattering in the SSS wave. It is found that the spin mutual information, entanglement and discord of the out-states, when averaged over the possible in-states, all vary in a similar way with respect to the relative momentum. The novel connection between emergent symmetry and spin entanglement found by a previous study [Phys. Rev. Lett. 122, 102001 (2019)] could then be extended naturally to spin correlations beyond entanglement.
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.
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.
Inspired by a recent Letter [S. R. Beane et al., Phys. Rev. Lett. 122, 102001 (2019)], the entanglement generated in the elastic SSS-wave scattering of p+3Hep+^{3}\mathrm{He}p+3He and n+3Hn+^{3}\mathrm{H}n+3H is studied, where the proton, neutron, 3He^{3}\mathrm{He}3He, and 3H^{3}\mathrm{H}3H are all regarded as qubits. To deal with the Coulomb interaction between the proton and 3He^{3}\mathrm{He}3He, we derive the entanglement power, a physical quantity that measures the average entanglement generated by a scattering process, for charged qubits within the screening method. The entanglement power in the aforementioned two few-nucleon scatterings is found to be generally much smaller than that in the SSS-wave n+pn+pn+p scattering at low energies, with the corresponding cluster effective field theories possessing an enhanced approximate $\text{SU}{(2)}_{1}\ensuremath{\bigotimes}\text{SU}{(2)}_{2}$ symmetry at leading order. Our study suggests that the entanglement generation capacities of effective interactions between nucleons and light nuclei could be more suppressed than realistic nucleon-nucleon interactions at low energies.
We investigate the spin entanglement in few-nucleon scattering processes involving nucleons and deuterons. For this purpose, we consider the entanglement power introduced by Beane et al. We analyze different entanglement entropies as a basis to define the entanglement power of the strong interaction and calculate the corresponding entanglement powers for proton-neutron, neutron-deuteron, proton-deuteron, and deuteron-deuteron scattering. For the latter two processes, we also take into account the modification from the Coulomb interaction. In contrast to proton-neutron scattering, no universal low-energy features are evident in the spin entanglement in neutron-deuteron, proton-deuteron, and deuteron-deuteron scattering.
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.