Entanglement Suppression, Quantum Statistics and Symmetries in Spin-3/2 Baryon Scatterings

We explore the interplay among entanglement suppression, quantum statistics and enhanced symmetries in the non-relativistic $S$-wave scattering involving the lowest-lying spin-3/2 baryons, which can be considered as four-dimensional qudits. These baryons form a ten-dimensional representation (decuplet) under the $\text{SU}(3)$ light-flavor symmetry and, in this limit, are considered indistinguishable under strong interactions. Treating the $S$-matrix in the spin-3/2 baryon-baryon scattering as a quantum logic gate in the spin space, we study the consequence of entanglement suppression and compute the entanglement power of the $S$-matrix. When the entanglement power vanishes, the $S$-matrix is either an Identity or a SWAP gate and spin-flavor symmetries and/or non-relativistic conformal invariance emerge, as previously observed in spin-1/2 baryons. In the case of scattering identical particles, the entanglement power never vanishes due to constraints from spin statistics, which we interpret as projection-valued measurements onto symmetric or antisymmetric Hilbert space and define the entanglement power accordingly. When the entanglement power is non-vanishing but sits at a global or local minimum, enhanced symmetries still emerge and the $S$-matrix can be interpreted as an Identity or a SWAP gate acting on the restricted Hilbert space allowed by quantum statistics. In general, when scattering identical spin-$s$ particles, we identify an enhanced $\text{SU}(2s+1)_{\text{spin}}$ symmetry for the Identity gate.

💡 Research Summary

This paper investigates the relationship between entanglement suppression, quantum statistics, and emergent symmetries in low‑energy, non‑relativistic S‑wave scattering of the lightest spin‑3/2 baryons (the decuplet). The authors treat each spin‑3/2 baryon as a four‑dimensional qudit, so that the two‑body S‑matrix acts as a two‑qudit quantum gate in spin space. The S‑matrix is decomposed into projectors onto irreducible representations of the spin SU(2) and flavor SU(3) groups, with associated phase shifts δ_{J F}(p) for each total‑spin J (0–3) and flavor channel F.

Entanglement power, defined as the average linear entropy generated by the gate over all product input states, serves as a state‑independent measure of a scattering process’s ability to create spin entanglement. For distinguishable particles, the entanglement power vanishes only when the S‑matrix reduces to either the Identity or the SWAP gate. In the Identity case the full SU(2s + 1){spin} × SU(3){flavor} symmetry (here SU(4){spin} × SU(3){flavor}) is restored; in the SWAP case the system exhibits non‑relativistic conformal (Schrödinger) symmetry.

When the two baryons are identical fermions, the Pauli principle restricts the physical Hilbert space to symmetric (spin‑flavor) or antisymmetric subspaces. Consequently the total entanglement power can never be zero. The authors therefore introduce a “projected entanglement power” that averages only over the allowed subspace. Even in this constrained setting, the projected entanglement power reaches a global (or local) minimum when the S‑matrix acts as Identity or SWAP within the allowed subspace, leading again to an enhanced SU(2s + 1)_{spin} symmetry (SU(4) for s = 3/2).

Group‑theoretic analysis of the decuplet‑decuplet product 10 ⊗ 10 yields irreps 1 ⊕ 8 ⊕ 27 ⊕ 64, each associated with specific (J,F) combinations. The authors show that equal phase shifts in the J = 0 and J = 3 channels enforce the Identity gate, while equality in the J = 1 and J = 2 channels yields the SWAP gate. These conditions correspond precisely to the vanishing or minimization of entanglement power.

The paper then validates these symmetry arguments within a non‑relativistic effective field theory (NREFT). At leading order the contact Lagrangian contains low‑energy constants (LECs) for each irrep; the phase shifts are directly related to these LECs. When the relevant LECs become equal (or vanish), the EFT reproduces the Identity or SWAP S‑matrix and the associated enhanced symmetry. In the large‑N_c limit, the decuplet baryons become degenerate and the required relations among LECs emerge automatically, providing a QCD‑based justification for entanglement suppression.

Phenomenologically, the authors discuss experimental and lattice QCD evidence for strong decuplet‑decuplet interactions, such as the ΔΔ dibaryon candidate d*(2380) and the ΩΩ system with a large scattering length (a ≈ 4.6 fm). These systems exhibit scattering parameters that place them near the entanglement‑power minima, supporting the conjecture that nature may favor configurations with reduced spin entanglement.

In the final sections the paper treats identical‑particle scattering in detail, constructing the reduced density matrix, computing the projected entanglement power, and demonstrating how the Identity or SWAP gates act on the symmetric/antisymmetric subspace. The analysis confirms that the enhanced SU(2s + 1)_{spin} symmetry identified for spin‑1/2 octet baryons extends naturally to spin‑3/2 decuplet baryons.

Overall, the work establishes entanglement suppression as a universal organizing principle for low‑energy hadronic scattering, linking information‑theoretic concepts to emergent symmetries in QCD. It opens avenues for future studies of higher‑spin qudits, relativistic extensions, and targeted lattice simulations to test the predicted symmetry enhancements.