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arXiv:2212.11092 · Physical Review C

Entanglement generation in few-nucleon scattering

Dong Bai, Zhongzhou Ren

Published Dec 21, 2022• 36 citations
arXivHTMLPDF

Abstract

Inspired by a recent Letter [S. R. Beane et al., Phys. Rev. Lett. 122, 102001 (2019)], the entanglement generated in the elastic $S$-wave scattering of $p+^{3}\mathrm{He}$ and $n+^{3}\mathrm{H}$ is studied, where the proton, neutron, $^{3}\mathrm{He}$, and $^{3}\mathrm{H}$ are all regarded as qubits. To deal with the Coulomb interaction between the proton and $^{3}\mathrm{He}$, 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 $S$-wave $n+p$ 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.

DOI
10.1103/physrevc.106.064005

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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 SU(2)1\ensuremath⨂SU(2)2\text{SU}{(2)}_{1}\ensuremath{\bigotimes}\text{SU}{(2)}_{2}SU(2)1​\ensuremath⨂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.
Abstract 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 study quantum resources in the spin degrees of freedom, such as entanglement, stabilizer magic, and non-local magic, in low-energy nucleon-nucleon scattering through next-to-leading order in pionless effective field theory. Treating each nucleon spin as a qubit, we calculate the corresponding resource-generating powers of the scattering operator at generic center-of-mass momentum and scattering angle ΘΘΘ. The analysis retains SSS- and PPP-wave channels generated by two-derivative contact interactions. When the microscopic physics exhibits Wigner's SU(4)SU(4)SU(4) spin-flavor symmetry, the neutron-proton amplitude becomes proportional to the spin-space identity operator and therefore generates no new resources after scattering, extending an observation previously made for leading-order SSS-wave scattering. The same-nucleon channel remains resource-generating because constraints from identical particles project out part of the Hilbert space. These results show how enhanced symmetries, partial-wave structure, and resource generation are intertwined in low-energy two-body scattering.
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.
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.
We study the connection between accidental symmetries in the nuclear interaction and spin entanglement in two-nucleon scattering. Specifically, we incorporate different levels of Wigner SU(4) and Serber symmetries into leading-order potentials derived from chiral effective field theory. We conduct a quantitative analysis by computing the full S matrix, demonstrating that the neutron-proton spin entanglement can be related to the symmetry properties of the interaction and the presence of certain operators and partial waves. Furthermore, we study the order-by-order evolution of the spin entanglement, up to next-to-next-to-leading order in Weinberg power counting, for both neutron-proton and neutron-neutron scattering. Entanglement suppression is not observed in neutron-neutron scattering, which can be attributed to the Pauli principle and the absence of accidental symmetries in this system. We conclude that entanglement is a useful guide for studying the power counting and symmetries in nuclear interactions derived from effective field theories.