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Antiflatness and nonlocal nonstabilizerness in two-particle scattering processes

Caroline E. P. Robin*

Martin J. Savage†,‡

  • InQubator for Quantum Simulation (IQuS), Department of Physics, University of Washington, Seattle, Washington 98195, USA

  • *Contact author: crobin@physik.uni-bielefeld.de
  • †Contact author: mjs5@uw.edu
  • ‡On leave from the Institute for Nuclear Theory, Seattle, Washington, USA.
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Phys. Rev. D 114, 014007 – Published 6 July, 2026

DOI: https://doi.org/10.1103/hvft-hk9p

Abstract

Nonlocal nonstabilizerness (NL NS) and antiflatness provide a measure of the quantum complexity in the wave function of a physical system. Supported by entanglement, they cannot be removed by local unitary operations, thus providing basis-independent measures, and sufficiently large values underpin the need for quantum computers in order to perform precise simulations of the system at scale. Towards a better understanding of the quantum-complexity generation by fundamental interactions, the building blocks of many-body systems, we consider nonlocal nonstabilizerness and antiflatness in two-particle scattering processes, specifically focusing on low-energy nucleon-nucleon scattering and high-energy Møller scattering. We find that the nonlocal nonstabilizerness induced in both interactions is four times the antiflatness (which is found to be true for any two-qubit wave function), and verify the relation between the Clifford-averaged antiflatness and total nonstabilizerness. For these processes, the antiflatness is a more experimentally accessible quantity as it can be determined from one of the final-state particles, and does not require spin correlations. While the Møller experiment at the Thomas Jefferson National Accelerator Facility does not include final-state spin measurements, the results presented here may add motivation to consider their future inclusion.

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Phys. Rev. D 114, 014007– Published 6 July, 2026
  • Received 19 January 2026
  • Accepted 26 May 2026
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