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
Θ. 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.
This paper explores the connections between particle scattering and quantum information theory in the context of the non-relativistic, elastic scattering of two spin-1/2 particles. An untangled, pure, two-particle in-state is evolved by an S-matrix that respects certain symmetries and the entanglement of the pure out-state is measured. The analysis is phrased in terms of unitary, irreducible representations (UIRs) of the symmetry group in question, either the rotation group for the spin degrees of freedom or the Galilean group for non-relativistic particles. Entanglement may occurs when multiple UIRs appear in the direct sum decomposition of the direct product in-state, but it also depends of the scattering phase shifts.
The entangling power of a unitary operator acting on a bipartite Hilbert space measures the entanglement it generates from product states, averaged over the inputs. A finite-dimensional unitary has a spectral decomposition
U=∑a=1neiθaPa, where
eiθa are the eigenvalues,
Pa the corresponding eigen-projectors, and
n is the number of distinct eigenvalues. After removing an overall phase, the entangling power is a function on the
(n−1)-torus of relative eigenphases at fixed spectral projectors. We prove that this function is stationary at all
2n−1 points on the torus where every relative phase is
0 or
π, which we define as \textit{corners}. Up to an overall phase,
U at each corner is a generalized reflection
R=I−2Q satisfying
R2=I, where
Q is the sum of spectral projectors whose relative phase is
π. At the corner the entangling power is expressed in terms of seven local-unitary invariants of
Q. A unitary gate
U can be realized as a corner of some projector family if and only if
U2∝I, a condition satisfied by many Clifford and non-Clifford gates. We illustrate the theorem with two-qubit gates,
SU(N) channel decompositions, and two-site spin chains, obtaining examples of minima, maxima, and saddle points. In addition, a corner that is a saddle point on the full phase torus can appear as a local maximum or minimum along different time-evolution trajectories.
Entanglement and magic are fundamental resources that capture the complexity of quantum many-body systems. Non-local magic isolates the irreducible nonstabilizerness intrinsically tied to entanglement. However, evaluating this quantity generally requires a prohibitive minimization over the full Hilbert space, making it computationally inaccessible beyond a few qubits. Here, we overcome this bottleneck by establishing a closed-form expression for the non-local stabilizer entropies of fermionic Gaussian states over local Gaussian unitaries, which we prove at Rényi index
α=2 for arbitrary subsystem size, and which can be evaluated in polynomial time directly from the eigenvalues of the reduced Majorana covariance matrix. We apply this framework to characterize fermionic non-local magic across diverse physical regimes: we derive an exact Page-like curve for typical random states, reveal logarithmic scaling at the quantum critical point of the XY model, and establish a quasiparticle picture for magic generation during out-of-equilibrium quantum quenches. Crucially, because our result relies solely on two-point correlation functions, it provides a scalable route for the experimental estimation of fermionic non-local magic in large-scale quantum processors via fermionic shadow tomography.
This paper investigates the dynamical generation of entanglement in scattering systems, in particular two spin systems that interact via rotationally invariant scattering. The spin degrees of freedom of the in states are assumed to be in unentangled, pure states, as defined by the entropy of entanglement. Because of the restriction of rotationally symmetric interactions, perfectly entangling
S matrices, i.e., those that lead to a maximally entangled out state, only exist for a certain class of separable in states. Using Clebsch-Gordan coefficients for the rotation group, the scattering phases that determine the
S matrix are determined for the case of spin systems with $\ensuremath{\sigma}=1∕2$, 1, and
3∕2.
We study two-body scattering as an SU(N)-equivariant map acting on tensor-product representation spaces and analyze the entanglement generated by the
S-matrix. This representation-theoretic perspective separates group structure from dynamics: the decomposition of
R⊗R′ fixes the invariant operator algebra and therefore the qualitative entangling power of the process. For particles in the fundamental representation,
EndSU(N)(N⊗N)=Span{I,S}, so only the identity and swap directions preserve separability, whereas generic combinations generate entanglement. Adjoint-adjoint scattering involves a larger invariant algebra involving
d-tensors and is intrinsically entangling. In Yang-Mills theory one can use color-kinematics duality to show that the color kernel lies on a fixed ray of this operator space, yielding a universal maximum of the outgoing entanglement for scattering at right angles,
E⋆(2)=43 for
SU(2) and
E⋆(3)≃0.91, independent of kinematics. Dimension-six operators preserve this universality, while dimension-eight deformations populate new color sectors and shift
E⋆(N), suggesting that entanglement in color space functions as a tomographic probe of effective operators. In helicity space, requiring maximally entangled inputs to scatter into maximally entangled outputs uniquely selects the Yang-Mills quartic coupling and enforces the color Jacobi identity, restating the on-shell Ward constraints as conditions on entanglement preservation. Our results suggest that the information-theoretic viewpoint unifies algebraic, geometric, and dynamical aspects of scattering.