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.
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.
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.
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≥2. 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≥2. 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.
Quantum entanglement and quantum nonstabilizerness are fundamental resources that characterize distinct aspects of a quantum state: Entanglement reflects nonlocal correlations, while nonstabilizerness quantifies the deviation from stabilizer states. A quantum state becomes a valuable resource for applications like universal quantum computation only when both quantities are present. Here, we propose that quantum nonlocal nonstabilizerness (NN) serves as an effective measure of this combined resource, incorporating both entanglement and nonstabilizerness. We demonstrate that NN can be precisely computed for two-qubit pure states, establishing a direct relationship with the entanglement spectrum. We then extend the definition of NN to mixed states and explore its presence in many-body quantum systems. We reveal that the two-point NN decays according to a power law in critical states, indicating that it can serve as an effective quantum information probe for phase transitions. Furthermore, we explore measurement-induced NN and uncover an intriguing phenomenon termed ``nonstabilizerness swapping,'' wherein post-measurement NN decays more slowly than any pre-measurement correlations. The occurrence of this phenomenon provides a sufficient condition for both entanglement swapping and the presence of a nontrivial sign structure. Our results thus represent a pivotal step toward accurately quantifying the ``quantumness'' of a state and bring insights from multiple perspectives to the property of NN.
Magic, or nonstabilizerness, is the resource that lifts Clifford circuits to universal quantum computation and has become a standard diagnostic of many-body states. For a state shared between two parties, however, a basic question has remained open: how much of the magic resides in the correlations between the parties rather than in their local bases? Isolating this nonlocal magic requires minimizing over all local bases, an optimization that has so far resisted exact solution. Here we solve it for the stabilizer fidelity: the nonlocal magic of every pure multiqubit state is the distance of its entanglement spectrum from the closest spectrum of Bell pairs. The same quantity governs an apparently unrelated task: a family of states universally embezzles entanglement under local operations and classical communication if and only if its nonlocal magic diverges. The deciding property is not the amount of entanglement but the way the entanglement spectrum spreads its weight across factor-of-two windows of rank, so that critical chains and random-singlet states, with identical logarithmic entanglement scaling, carry unbounded and vanishing nonlocal magic, respectively. Nonlocal magic thereby becomes an operationally meaningful property of quantum correlations, directly accessible to tensor-network simulations and, through entanglement spectroscopy, to experiments.
We explore the concept of antiflatness to characterize the structural fluctuations within the entanglement spectrum of a quantum state (i.e., the spectrum of its reduced density operator). As a measure of the interplay between entanglement and magic, two fundamental quantum resources, antiflatness provides second-order information about quantum correlations that standard average measures fail to capture. Recognizing that standard majorization theory fundamentally orders states by purity and is structurally blind to spectral fluctuations, we introduce a novel partial ordering known as antiflat majorization, based on the Rényi entropy spread. We define Flatness-Preserving Operations (FPOs), establishing new necessary conditions for state convertibility. Furthermore, we unify different measures of antiflatness-such as Capacity of Entanglement, Linear Rényi spread, and Logarithmic antiflatness-using the frameworks of escort distributions and Bregman divergences. We prove that the Capacity of Entanglement can be expressed as a second derivative of the Kullback-Leibler divergence along the escort trajectory, connecting it with the Quantum Fisher Information. Finally, we demonstrate that absolute maximal antiflatness is not achieved by a single universal state, but rather by a continuous Pareto frontier of extremal states with jump spectra, and we analyze the typicality of these spectral fluctuations using Haar, Bures-Hall and t-doped Clifford random state ensembles.
Toward an improved understanding of the role of quantum information in nuclei and exotic matter, we examine the quantum magic (nonstabilizerness) in low-energy strong interaction processes. As stabilizer states can be prepared efficiently using classical computers, and include classes of entangled states, it is quantum magic and fluctuations in quantum magic, together with entanglement, that determine computational resource requirements. As a measure of fluctuations in quantum magic, and hence the severity of the exponentially scaling classical computing resource requirements, induced by scattering, the “magic power” of the 𝑆-matrix is introduced. This provides indirect experimental constraints on quantum resources required to model nuclei and dense matter using fault-tolerant quantum computers. Using experimentally determined scattering phase shifts and mixing parameters, the magic power in nucleon-nucleon and hyperon-nucleon scattering, along with the magic in the deuteron, are found to exhibit interesting and distinct features. The Σ−-baryon is identified as a potential candidate catalyst for enhanced spreading of magic and entanglement in dense matter, depending on in-medium decoherence.