Local universality of non-local quantum resources in rotationally invariant scattering
Abstract
Elastic scattering can generate entanglement and non-local magic between the spins of the two outgoing particles. The amount of entanglement and magic produced is encoded in the S-matrix; a unitary quantum gate that acts on the joint Hilbert space of the two spin-J particles. Previous work derived the entanglement power in terms of the scattering phase shifts for rotationally invariant S-matrices with J=1/2,1,3/2. In this paper, a closed form solution is derived for all J. We further prove that a broad class of non-local quantum resources depend to leading order only on the squared projective Hilbert-Schmidt distance from the nearest non-entangling gate. This holds for the entanglement power and non-local magic power, and the choice of resource simply changes the overall normalization. This universality establishes a common geometric origin for the leading resource-generating capacity of scattering, independent of the details of the interaction.
Related
- Finite-rank multiplicative perturbations of rotationally invariant non-Hermitian random matrices
- Spectral properties of deterministic matrices multiplied by rotationally invariant random non-Hermitian ensembles
- Ghost rotationally invariant slave-boson approach to response functions
- Synchronous and asynchronous Monte Carlo dynamics of mean-field spin glasses with rotationally invariant couplings: what they share and where they differ
- Information-Theoretic Limits for Rectangular Spiked Matrix Models with Rotationally Invariant Noise
BibTeX
@misc{beane2026local,
title = {{Local universality of non-local quantum resources in rotationally invariant scattering}},
author = {Silas R. Beane and Roland C. Farrell},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.06791},
eprint = {2610.06791},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.06791},
}
RIS
TY - UNPB
TI - Local universality of non-local quantum resources in rotationally invariant scattering
AU - Silas R. Beane
AU - Roland C. Farrell
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.06791
UR - https://arxiv.org/abs/2610.06791
AB - Elastic scattering can generate entanglement and non-local magic between the spins of the two outgoing particles. The amount of entanglement and magic produced is encoded in the S-matrix; a unitary quantum gate that acts on the joint Hilbert space of the two spin-J particles. Previous work derived the entanglement power in terms of the scattering phase shifts for rotationally invariant S-matrices with J=1/2,1,3/2. In this paper, a closed form solution is derived for all J. We further prove that a broad class of non-local quantum resources depend to leading order only on the squared projective Hilbert-Schmidt distance from the nearest non-entangling gate. This holds for the entanglement power and non-local magic power, and the choice of resource simply changes the overall normalization. This universality establishes a common geometric origin for the leading resource-generating capacity of scattering, independent of the details of the interaction.
ER -