Quantum nonlocal nonstabilizerness

Faidon Andreadakis, Paolo Zanardi A

Harshank Shrotriya

Faidon Andreadakis, Paolo Zanardi A

Nonstabilizerness is a quantum property of states associated with the non-Clifford resources required for their preparation. As a resource, nonstabilizerness complements entanglement, and the interplay between these two concepts has garnered significant attention in recent years. In this work, we establish an exact correspondence between the generation of nonlocal nonstabilizerness and operator entanglement under unitary evolutions. Nonlocal nonstabilizerness refers to nonstabilizerness that cannot be erased via local operations, while operator entanglement generalizes entanglement to operator space, characterizing the complexity of operators across a bipartition. Specifically, we prove that a unitary map generates nonlocal nonstabilizerness if and only if it generates operator entanglement on Pauli strings. Guided by this result, we introduce an average measure of a unitary's Pauli-entangling power, serving as a proxy for nonlocal nonstabilizerness generation. We derive analytical formulas for this measure and examine its properties, including its typical value and upper bounds in terms of the nonstabilizerness properties of the evolution.

Lei-Yi-Nan Liu, Jian Cui

Nonlocal nonstabilizerness quantifies the irreducible magic resource encoded in bipartite entanglement, but its evaluation is generally hindered by a highly nonconvex optimization over local unitary transformations. Here we propose a Schmidt-reference-state framework that replaces this optimization by a direct construction from the sorted Schmidt spectrum. We conjecture that the nonlocal stabilizer Rényi entropy (SRE) is given by the SRE of the corresponding reference state, and support this conjecture through analytical and numerical evidences. Our framework makes nonlocal nonstabilizerness efficiently accessible for weakly entangled many-body states whenever the entanglement spectrum is available. Applying it to Haar-random states, critical spin chains, and PXP dynamics, we show that nonlocal SRE captures nonstabilizer structures in the entanglement spectrum that are invisible to conventional entanglement measures. Our results establish entanglement spectra as a powerful window into irreducible nonstabilizer correlations, opening a broadly applicable route to studying nonlocal magic resources of quantum many-body systems in and out of equilibrium.

Lei-Yi-Nan Liu, Jian Cui

Entanglement and nonstabilizerness capture distinct aspects of quantum complexity, yet their relation through the entanglement spectrum remains poorly understood. Here we develop a spectral framework for bipartite nonlocal nonstabilizerness. We introduce a generalized anti-flatness and derive upper and lower bounds on the nonlocal stabilizer Rényi entropy (SRE) in terms of Rényi entanglement entropy and spectral non-uniformity. We further reduce the local-unitary optimization to a single-unitary problem and prove that the ordered Schmidt reference state is a local minimum of the SRE for integer $α\geq2$. Applying these results to exponentially and algebraically decaying spectra reveals parametrically distinct relations between entanglement and nonlocal nonstabilizerness. For broad spectra, we introduce a dyadic-shell sandwich construction that determines the asymptotic SRE scaling. At one-dimensional conformal critical points, it yields a universal hierarchy of double-logarithmic scaling laws for integer $α\geq2$. Our spectral bounds and dyadic-shell sandwich construction provide general tools for analyzing nonlocal SRE, offering a flexible framework that can be applied to a wide range of entanglement spectra in quantum many-body systems.

Caroline Robin, Martin J. Savage A

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.