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arXiv:2506.08960 · Physical Review Research

Entanglement suppression, quantum statistics, and symmetries in spin-3/2 baryon scatterings

Tao-Ran Hu, Katsuyoshi Sone, Feng-Kun Guo, Tetsuo Hyodo, Ian Low

Published Nov 14, 2025• 6 citations

Abstract

We explore the interplay among entanglement suppression, quantum statistics, and enhanced symmetries in the nonrelativistic 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 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 nonrelativistic 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 nonvanishing 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 SU ( 2 s + 1 ) spin symmetry for the Identity gate.

DOI: 10.1103/x52w-4rbs

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We explore the interplay among entanglement suppression, quantum statistics, and enhanced symmetries in the nonrelativistic 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 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 nonrelativistic 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 nonvanishing 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 SU ( 2 s + 1 ) spin symmetry for the Identity gate.

We study entanglement suppression in

s

-wave

ΩΩ

scattering, where each baryon has spin

3/2

. By treating the

S

-matrix as a quantum operator acting on the spin states, we quantify its ability to generate entanglement and identify the conditions on the phase shifts of the spin channels that minimize entanglement generation in the system. In

ΩΩ

scattering, only antisymmetric spin channels are allowed due to Fermi-Dirac statistics. Applying the entanglement-suppression framework to

ΩΩ

scattering, we find two solutions for the phase shifts: one leading to a spin SU(4) symmetry and the other to a nonrelativistic conformal symmetry. We show that the solution associated with the nonrelativistic conformal symmetry originates from the specific structure of the Clebsch-Gordan coefficients in the

3/2 \otimes 3/2

system.

Symmetry is among the most fundamental and powerful concepts in nature, whose existence is usually taken as given, without explanation. We explore whether symmetry can be derived from more fundamental principles from the perspective of quantum information. Starting with a two-qubit system, we show there are only two minimally entangling logic gates: the identity and the

\mathrm{SWAP}

, which interchanges the two states of the qubits. We further demonstrate that, when viewed as an entanglement operator in the spin-space, the

S

-matrix in the two-body scattering of fermions in the

s

-wave channel is uniquely determined by unitarity and rotational invariance to be a linear combination of the identity and the

\mathrm{SWAP}

. Realizing a minimally entangling

S

-matrix would give rise to global symmetries, as exemplified in Wigner's spin-flavor symmetry and Schr\"odinger's conformal invariance in low energy quantum chromodynamics. For

{N}_{q}

species of qubit, the identity gate is associated with an

[SU(2){]}^{{N}_{q}}

symmetry, which is enlarged to

SU(2{N}_{q})

when there is a species-universal coupling constant.

The entangling power of a unitary operator quantifies its ability to generate entanglement from product states and provides a natural probe of quantum many-body dynamics. Entanglement extremization at points of enhanced symmetry has previously been observed in high-energy scattering. In this work we compute the time-averaged entangling power of anisotropic Heisenberg spin chains across two-site models and finite-size systems, as well as the entangling power of the two-magnon

S

-matrix in the thermodynamic limit. For two-site models we establish a monotonic hierarchy: the entangling power decreases as the symmetry group grows, reaching its minimum at the

SU(2)

XXX point. Finite-size XXZ chains exhibit sharp dips at the

SU(2)

points

Δ=\pm 1

and the free-fermion point

Δ=0

, with the free-fermion dip decaying much more slowly with system size. In the thermodynamic limit, we decompose the two-magnon

S

-matrix into quantum logic gates -- Identity, SWAP, and

σ_z\otimesσ_z

-- and show that the entangling power vanishes for all scattering energies at the

SU(2)

points, where the

S

-matrix reduces to the Identity gate, while the free-fermion point achieves the maximum -- the opposite of the finite-size many-body behavior. The entangling power can serve as an {\em operator} diagnostic for symmetry and selected aspects of integrability in quantum simulations of spin-chain dynamics.

We present a general framework connecting global symmetries to the relativistic

S

-matrix through the lens of quantum information theory. Analyzing the 2-to-2 scattering of particles of any helicity, we systematically characterize relativistic scattering amplitudes as quantum gates in the bipartite space of states with a discrete quantum number. This formalism naturally recovers and significantly extends previous results on entanglement suppression of the

S

-matrix, providing a comprehensive approach for studying the emergence of symmetries from an information-theoretic perspective. As a central result, we show that constraining the

S

-matrix to the span of minimally entangling operators is equivalent to realizing an emergent

SU(N)

global symmetry.

We study the interplay between crossing symmetry and entanglement in

2 \to 2

scattering within local quantum field theories that possess an

SU(N)

global symmetry. In particular, we recast scattering amplitudes of fixed helicity as quantum operations on the Hilbert space of internal quantum numbers, where the external states play the role of qudits. The entire space of

SU(N)

-invariant scattering operators between qudits is spanned by a minimal set of three quantum gates. Recoupling relations among quantum gates are shown to follow directly from the crossing properties of the underlying amplitudes and reveal that entanglement generated from separable states in one channel is necessarily intertwined with another. Consequently, we argue any interacting quantum field theory that realizes an

S

global symmetry must generate entanglement in at least one scattering channel.

The concept of quantum information has provided new ways to investigate the theoretical structure of particle interactions. In particular, it has been shown that extrema of quantum entanglement in scattering and decay processes can be related to symmetries and characteristic properties of particles. We focus on a more specific question: whether the minimization of entanglement entropy generated in scattering processes is systematically related to the suppression of interactions that violate global symmetries or selection rules. We conjecture that the minimization of the entanglement entropy can select the symmetry-preserving point when a new interaction opens a symmetry-violating scattering channel. We investigate the plausibility of this conjecture by considering interactions beyond the Standard Model (BSM) that violate global symmetries or the corresponding selection rules, including lepton number violation, baryon number violation, lepton flavor violation, and flavor-changing neutral currents. We show that, when symmetry-violating interactions open final-state sectors that are orthogonal to the symmetry-preserving sector, the symmetry-preserving point becomes a local minimum of the entanglement entropy. Our results support the possibility that the minimization of entanglement provides a common information-theoretic principle underlying the suppression of BSM phenomena relevant to symmetry-violating interactions.