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arxiv: 2606.17148 · v1 · pith:GJKKPAWWnew · submitted 2026-06-15 · ⚛️ nucl-th · hep-ph· quant-ph

Quantum Resources and Wigner Symmetry in Nucleon-Nucleon Scattering from Effective Field Theory

Ian Low , Thomas R. Richardson , Sokratis Trifinopoulos This is my paper

Pith reviewed 2026-06-27 02:22 UTC · model grok-4.3

classification ⚛️ nucl-th hep-phquant-ph
keywords nucleon-nucleon scatteringWigner SU(4) symmetryquantum resourcespionless effective field theoryspin qubitsentanglement generationpartial waves
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The pith

Wigner's SU(4) symmetry reduces the neutron-proton scattering amplitude to the spin identity operator, generating no new quantum resources.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper calculates how quantum resources such as entanglement and magic arise in the spin degrees of freedom during low-energy nucleon-nucleon scattering, using the pionless effective field theory through next-to-leading order while retaining S- and P-wave contact terms. It shows that exact Wigner SU(4) spin-flavor symmetry forces the neutron-proton amplitude to be proportional to the identity in spin space, so the outgoing state carries exactly the same resources as the incoming state. This protection extends an earlier leading-order S-wave result to higher partial waves and generic kinematics. In the identical-nucleon channel the symmetry does not eliminate resource generation because the Pauli principle projects out part of the two-qubit space. The analysis therefore links enhanced symmetry, partial-wave content, and resource production in a single two-body scattering process.

Core claim

When the microscopic physics respects Wigner's SU(4) symmetry the neutron-proton scattering amplitude becomes proportional to the spin-space identity operator and therefore generates no new resources after scattering; the same-nucleon channel remains resource-generating because identical-particle constraints remove part of the Hilbert space. This holds at generic center-of-mass momentum and scattering angle when only the two-derivative contact interactions of the NLO pionless EFT are retained.

What carries the argument

The NLO pionless EFT scattering operator in the two-qubit spin space, made proportional to the identity by exact SU(4) symmetry.

If this is right

  • Neutron-proton scattering under exact SU(4) leaves the resource content of any incoming spin state unchanged.
  • Scattering of identical nucleons still produces resources because antisymmetrization removes half the two-qubit space.
  • The resource-neutral result for neutron-proton scattering persists at all angles and momenta once only two-derivative contacts are kept.
  • All three resource measures (entanglement, stabilizer magic, non-local magic) simultaneously vanish for the neutron-proton channel under the symmetry.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Approximate SU(4) symmetry in real nuclear forces may suppress but not completely eliminate resource generation in neutron-proton scattering.
  • The same symmetry argument could be applied to three-nucleon systems to identify channels where quantum resources remain protected.
  • Quantum simulators of nuclear physics could exploit the symmetry-protected channels to reduce the overhead of simulating spin entanglement.

Load-bearing premise

Each nucleon spin can be treated as an independent qubit whose resource measures are completely determined by the S- and P-wave contact amplitudes of the NLO pionless EFT.

What would settle it

Explicit computation of the entanglement or magic measures for a realistic nucleon-nucleon potential that exactly enforces SU(4) symmetry and observation of nonzero resource generation in the neutron-proton channel at low momentum.

Figures

Figures reproduced from arXiv: 2606.17148 by Ian Low, Sokratis Trifinopoulos, Thomas R. Richardson.

Figure 1
Figure 1. Figure 1: FIG. 1. Entanglement power [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Same as Fig [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Same as Fig [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
read the original abstract

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 $\Theta$. The analysis retains $S$- and $P$-wave channels generated by two-derivative contact interactions. When the microscopic physics exhibits Wigner's $SU(4)$ 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 $S$-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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 3 minor

Summary. The paper examines quantum resources (entanglement, stabilizer magic, non-local magic) in low-energy nucleon-nucleon scattering at next-to-leading order in pionless EFT. Treating nucleon spins as qubits, it computes the resource-generating power of the scattering operator at generic center-of-mass momentum and angle, retaining S- and P-wave channels from two-derivative contact interactions. Under exact Wigner's SU(4) symmetry the neutron-proton amplitude is proportional to the spin-space identity operator and therefore generates no new resources, extending a prior leading-order S-wave observation; the same-nucleon (pp/nn) channels remain resource-generating because identical-particle projections break the proportionality.

Significance. If the central algebraic result holds, the work demonstrates how an enhanced symmetry in the NLO contact Lagrangian directly suppresses quantum resource generation in two-body scattering, independent of the values of the low-energy constants. This provides a clean, parameter-free illustration of the interplay between EFT operator structure, partial-wave content, and quantum-information measures, extending earlier LO results in a controlled way.

minor comments (3)
  1. [Abstract] The abstract states that the np amplitude 'becomes proportional to the spin-space identity operator' but does not indicate the explicit operator basis or the projection used for the identical-particle channels; adding one sentence referencing the relevant contact Lagrangian terms would improve clarity.
  2. The qubit encoding of the two-nucleon spin space is introduced without a brief reminder of the standard 4-dimensional basis (e.g., |↑↑⟩, |↑↓⟩, …); a short parenthetical definition in the first paragraph of the methods section would aid readers outside quantum information.
  3. Figure captions should explicitly state whether the plotted resource measures are evaluated at fixed momentum or integrated over angle, and whether the SU(4) limit is shown as a separate curve or as a limiting case.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive assessment of our work and the recommendation for minor revision. The report contains no specific major comments to address point by point.

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained

full rationale

The central claim follows algebraically from imposing exact SU(4) symmetry on the two-derivative contact operators in the NLO pionless EFT Lagrangian, which forces the np T-matrix to be proportional to the spin-space identity by representation theory; this holds for any values of the LECs and is independent of data fitting or prior results. The note that the result extends an LO observation is incidental and not load-bearing for the NLO derivation or resource calculation. No step equates a prediction to a fitted input by construction, renames a known result, or relies on a self-citation chain whose content is unverified outside the paper. The qubit encoding and resource measures are applied to the resulting operator in a standard way.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the applicability of pionless EFT at NLO and on the standard definitions of quantum resources; no new free parameters or invented entities are introduced in the abstract.

axioms (2)
  • domain assumption Pionless effective field theory truncated at next-to-leading order accurately describes low-energy nucleon-nucleon scattering in S- and P-waves
    The abstract states that the analysis retains S- and P-wave channels generated by two-derivative contact interactions within this framework.
  • domain assumption Nucleon spins may be treated as qubits for the purpose of calculating entanglement, stabilizer magic, and non-local magic
    The abstract opens with the statement that each nucleon spin is treated as a qubit.

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discussion (0)

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Reference graph

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