All standard scalar quantum-information measures -- concurrence, negativity, entanglement entropy, the optimized CHSH bound, and quantum Fisher information -- are CP-blind in ideal \\ spin-0 $\to f\bar f$ decays because the two-qubit spin state is maximally entangled for every CP angle. We show that stabilizer magic, fixed in the physical Pauli frame of spin analysis, escapes this blind spot: the stabilizer Rényi entropy admits an exact closed form, vanishing at CP-definite and Clifford phases and peaking at maximal non-Clifford mixing. Two experimentally accessible, magic-inspired CP witnesses follow; the linear amplitude is $14.3\times$ more efficient than its quartic counterpart and reaches discovery-level sensitivity at the HL-LHC for $H\toτ^+τ^-$.
All standard scalar quantum-information measures -- concurrence, negativity, entanglement entropy, the optimized CHSH bound, and quantum Fisher information -- are CP-blind in ideal \ spin-0 →ffˉ decays because the two-qubit spin state is maximally entangled for every CP angle. We show that stabilizer magic, fixed in the physical Pauli frame of spin analysis, escapes this blind spot: the stabilizer Rényi entropy admits an exact closed form, vanishing at CP-definite and Clifford phases and peaking at maximal non-Clifford mixing. Two experimentally accessible, magic-inspired CP witnesses follow; the linear amplitude is 14.3× more efficient than its quartic counterpart and reaches discovery-level sensitivity at the HL-LHC for H→τ+τ−.
Magic and entanglement are independent quantum resources, yet their exact relation in many-body dynamics has remained elusive. We uncover two structural principles. First, at any stabilizer state, the curvature of the second stabilizer Rényi entropy under an arbitrary Hermitian generator equals the quantum Fisher information up to a fixed normalization, creating a bidirectional bridge between computational and metrological resources. Second, for commuting Ising evolution on any forest graph, a Clifford pruning circuit yields the full stabilizer-Rényi family at arbitrary size and in any spatial embedding, thereby furnishing a graph-theoretic construction of families with finite magic density and vanishing entanglement density in the thermodynamic limit. We solve two paradigmatic one-dimensional realizations central to quantum simulation -- an Ising quench and a kicked Floquet chain -- exactly for arbitrary system size and directly in the thermodynamic limit, revealing finite magic density with vanishing entanglement density, distinct magic and entanglement revival periods, and Clifford points with zero magic but finite bipartite entanglement. The same tangent geometry fixes initial growth, perturbative revival lifting, and stability of thermodynamic magic minima. Large-scale Pauli-basis matrix-product-state calculations verify all predictions, and the tangent bridge yields a concrete protocol for detecting magic through established quantum-Fisher-information measurements.
Stabilizer Rényi entropy quantifies magic relative to a complete Pauli frame. In settings such as helicity states of massless particles, unsynchronized qubit registers, energy eigenbases, and systems under superselection rules, the computational basis may be fixed while the transverse Pauli axes remain unspecified. The stabilizer Rényi entropy then depends on the choice of those axes. We define a phase-averaged stabilizer Rényi entropy by averaging the Pauli moments before taking the logarithm. It is exactly invariant under independent local rephasings. For pure states, it vanishes precisely when the state is a stabilizer state in every phase convention. For a broad class of sparse supports, it reduces to a closed-form function of the basis-state probabilities alone. Within this class, the ceiling for n channels is ln[n3/(6n−5)] for n≥3 and ln57 for two channels. We apply the invariant to tree-level gluon scattering at four and five points, where the helicity-basis phases are unspecified. It saturates the two- and three-channel ceilings: ln57 at four points and ln1327 in 3→2 scattering. In same-helicity 2→3 scattering, it lies between a floor of ln78 and a ceiling of ln125184, reached in the resolved soft limit and particular collinear limits, respectively. In every configuration studied, the invariant is independent of the fixed external colors.
Stabilizer states constitute an important class of quantum states that can be generated from computational-basis states using Pauli operators and Clifford gates. Although they may exhibit substantial multipartite entanglement, quantum circuits restricted to stabilizer operations can be efficiently simulated classically and therefore cannot, by themselves, provide a quantum computational advantage. Such an advantage requires non-stabilizer resources, commonly referred to as quantum magic. In this paper, we investigate the non-stabilizerness of quantum states arising in a class of spin Hamiltonians by computing their stabilizer Rényi entropies. Using real-space renormalization-group techniques, we obtain a closed-form expression valid in the low-energy, large-distance regime. We analyze how quantum magic evolves under coarse-graining and explore its behavior across different parameter regimes and quantum phases.
Magic -- the resource enabling quantum computational advantage beyond stabilizer circuits -- has a clean phase-space characterization in odd prime dimensions that qubits notoriously lack. We study C(rho), the l_1 distance from a state's discrete Wigner function to the stabilizer polytope, and determine its exact geometry. For a single qubit with Bloch vector r we prove the closed form C = max(0, ||r||_1 - 1)/2, so the maximum is (sqrt(3)-1)/2, attained at the eight face states. For products of single-qubit states, C(rho_1 x ... x rho_n) <= prod_i (1 + C(rho_i)) - 1, with equality whenever every factor has Bloch sign product r_x r_y r_z <= 0; this includes the exact tensor powers ((1+sqrt(3))/2)^n - 1 and the exact maximum of C over fully separable n-qubit states.
Because no discrete Wigner function for qubits is Clifford covariant, any such measure is frame dependent, and we identify which of its features are not. For a single qubit there are exactly two valid frames up to phase-space translation and C is identical on both. Pauli-covariant two-qubit frames number 2048 up to translation, and across them the ratio C(rho_Rx)/C(rho_Ry) takes the values 1/2, 1 and 2. In every one of these frames some stabilizer state has negative Wigner entries, a consequence of the Mermin-Peres square, so the two-qubit bound Gamma >= 1 + C/2 against the robustness of magic Gamma is frame independent.
Within the Wootters frame we prove integer values 1, 2, 1 of the tightness ratio kappa := (Gamma-1)/C for three families in the two-qubit repetition codespace, with explicit certificates. For n-qubit GHZ phase states we prove Gamma = |sin phi| + |cos phi| for all n and C >= 2^(floor(n/2)-1) (|sin phi| + |cos phi| - 1), tight for n = 2 and, by exact linear programming, for n = 3, 4, so kappa decays exponentially. Finally, C is not a magic monotone, so it cannot replace Gamma in distillation bounds.
Measures of non-stabilizerness (``magic'') of a quantum evolution quantify how hard it is to simulate on a classical computer. A natural question is how to extract information about magic from physical correlators, for example at finite temperature or in the ground state. In this paper we show how to measure magic using out-of-time-order correlators evaluated in an arbitrary state. For every full-rank state, and in particular for every Gibbs state, the resulting quantity vanishes if and only if the evolution is Clifford. We establish its basic properties, relate it to the stabilizer entropy of the Choi state, and prove that, even with a single fixed probe operator, it gives a lower bound on the number of T gates needed to implement the dynamics in any circuit architecture.
Quantum magic is a necessary resource for fault-tolerant quantum computing, capturing the departure of quantum states from the classically simulable stabiliser set. Motivated by its role in quantum information processing, we investigate the correlation structure of states that maximize the Rényi stabiliser entropies, focusing on the T-type and Hoggar states. Inspired by their distinctive properties, we explore the notion of Pauli flat states, defined as N-qubit states whose expectation values on all Pauli strings are equal in absolute value. These states reproduce the correlation structure of highly magical states, which could also be interpreted as a mixed variant of Pauli covariant N-qubit symmetric informationally complete (SIC) Weyl-Heisenberg fiducial states, while not necessarily possessing nontrivial quantum magic. We investigate their existence and possible constructions, including examples both inside and outside of the stabiliser polytope. To identify the latter, we examine a magic witness tailored to the introduced family of states. Finally, we discuss their entanglement and Bell nonlocality, providing a broader characterization of their quantum properties. For completeness, we find pure states with a relaxed condition on the Pauli expectations, which forces unequal elements to zero, and discuss their non-stabiliserness. Our results offer a new perspective on the relation between quantum magic and Pauli correlation structures. They hold relevance to geometrical approaches to quantum mechanics, entanglement and magic detection, as well as estimation tasks.