The Triangle Criterion detects mixed-state magic, proves multi-qubit distillation is strictly stronger than single-qubit schemes, and identifies a purity bound plus undetectable unfaithful magic states.
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In the large-N limit of the SYK model, quantum magic of pure KM states dual to black holes is linear in N with a temperature-tunable slope between 0 and 1/2.
Above a critical noise strength, operator scrambling in random circuits is suppressed leading to classical simulability; below it, simulation stays exponentially hard.
Nonlocal magic in fermionic Gaussian states is bounded by the entanglement spectrum of the covariance matrix, is extensive in the Haar ensemble, peaks at criticality in the Kitaev chain, and grows diffusively under random circuits.
Unitaries have an exactly quantifiable purity-constrained imaginarity-generating power that depends on intrinsic unitary properties and concentrates near its maximum for typical Haar-random dynamics in high dimensions.
Exact results show U(1) symmetry substantially suppresses non-stabilizerness in random states, with different leading scaling from entanglement near zero charge density.
Stabilizer Rényi entropy of 3-uniform hypergraph states equals a matrix-rank expression, cutting computation from exponential in 3N to polynomial in N times exponential in N.
Analytical and numerical study of stabilizer nullity and Rényi entropies in monitored Clifford circuits shows quantized decay for computational measurements and size-dependent relaxation to a non-trivial steady state for rotated bases.
Eigenstates in interacting integrable models match random superpositions of polynomially many Gaussian states for entanglement and non-Gaussianity, while nonintegrable models match exponentially many.
Mutual information between non-contractible regions on the torus fully classifies long-range nonstabilizerness for toric-code states but leaves a finite subset undetected in the doubled-Fibonacci string-net model.
Conservation laws in quantum circuits and Hamiltonians replace logarithmic coherence saturation with slow hydrodynamic relaxation globally and produce algebraic peak-time growth locally, unlike ergodic cases.
A complexity quantifier for stabilizer quantum states is defined via Jordan and Lie products and linked to nonstabilizerness via the L^4-norm of characteristic functions.
For weakly- and moderately-correlated molecular Hamiltonians, 2-stabilizer Renyi entropy of ground states scales linearly with both Hartree-Fock overlap and recovered correlation energy, with the link holding under contextual subspace approximations until the Coulson-Fischer point.
Within a restricted low-energy spin-sector ansatz for n-p scattering, direction-averaged magic is locally minimized at the CP-conserving point heta-bar=0 when the effective phase equals heta/4 or lies in specific windows.
Non-stabilizerness in the Hubbard dimer is quantified via robustness of magic and stabilizer Renyi entropy, revealing the latter's failure on mixed states and distinguishing it from non-Gaussianity and superselected entanglement.
Geometric study of non-stabilizerness in few-qubit systems via trace distance to the stabilizer polytope, with state sampling, measure comparisons, an analytical expression, facet classification, and a concentration bound linking it to entanglement.
citing papers explorer
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Triangle Criterion: a mixed-state magic criterion with applications in distillation and detection
The Triangle Criterion detects mixed-state magic, proves multi-qubit distillation is strictly stronger than single-qubit schemes, and identifies a purity bound plus undetectable unfaithful magic states.
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Tuning quantum magic of pure quantum chaotic states with a gravity dual
In the large-N limit of the SYK model, quantum magic of pure KM states dual to black holes is linear in N with a temperature-tunable slope between 0 and 1/2.
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Noise-induced Simulability Transition from Operator Scrambling
Above a critical noise strength, operator scrambling in random circuits is suppressed leading to classical simulability; below it, simulation stays exponentially hard.
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Nonlocal nonstabilizerness in free fermion models
Nonlocal magic in fermionic Gaussian states is bounded by the entanglement spectrum of the covariance matrix, is extensive in the Haar ensemble, peaks at criticality in the Kitaev chain, and grows diffusively under random circuits.
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Imaginarity-generating power of unitaries: A resource-theoretic approach
Unitaries have an exactly quantifiable purity-constrained imaginarity-generating power that depends on intrinsic unitary properties and concentrates near its maximum for typical Haar-random dynamics in high dimensions.
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Non-stabilizerness and U(1) symmetry in chaotic many-body quantum systems
Exact results show U(1) symmetry substantially suppresses non-stabilizerness in random states, with different leading scaling from entanglement near zero charge density.
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Stabilizer R\'enyi entropy of 3-uniform hypergraph states
Stabilizer Rényi entropy of 3-uniform hypergraph states equals a matrix-rank expression, cutting computation from exponential in 3N to polynomial in N times exponential in N.
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Rise and fall of nonstabilizerness via random measurements
Analytical and numerical study of stabilizer nullity and Rényi entropies in monitored Clifford circuits shows quantized decay for computational measurements and size-dependent relaxation to a non-trivial steady state for rotated bases.
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One-Body Purity, Non-Gaussianity, and Entanglement in Interacting Integrable Models
Eigenstates in interacting integrable models match random superpositions of polynomially many Gaussian states for entanglement and non-Gaussianity, while nonintegrable models match exponentially many.
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Long-range nonstabilizerness of topologically encoded states from mutual information
Mutual information between non-contractible regions on the torus fully classifies long-range nonstabilizerness for toric-code states but leaves a finite subset undetected in the doubled-Fibonacci string-net model.
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Coherence dynamics in quantum many-body systems with conservation laws
Conservation laws in quantum circuits and Hamiltonians replace logarithmic coherence saturation with slow hydrodynamic relaxation globally and produce algebraic peak-time growth locally, unlike ergodic cases.
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Complexity of quantum states in the stabilizer formalism
A complexity quantifier for stabilizer quantum states is defined via Jordan and Lie products and linked to nonstabilizerness via the L^4-norm of characteristic functions.
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Correlation is magic in electronic structure Hamiltonians
For weakly- and moderately-correlated molecular Hamiltonians, 2-stabilizer Renyi entropy of ground states scales linearly with both Hartree-Fock overlap and recovered correlation energy, with the link holding under contextual subspace approximations until the Coulson-Fischer point.
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Local Minimum of Spin-Sector Magic at the CP-Conserving Point in Low-Energy Neutron-Proton Scattering
Within a restricted low-energy spin-sector ansatz for n-p scattering, direction-averaged magic is locally minimized at the CP-conserving point heta-bar=0 when the effective phase equals heta/4 or lies in specific windows.
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Quantum magic of strongly correlated fermions $-$ the Hubbard dimer
Non-stabilizerness in the Hubbard dimer is quantified via robustness of magic and stabilizer Renyi entropy, revealing the latter's failure on mixed states and distinguishing it from non-Gaussianity and superselected entanglement.
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A trace distance-based geometric analysis of the stabilizer polytope for few-qubit systems
Geometric study of non-stabilizerness in few-qubit systems via trace distance to the stabilizer polytope, with state sampling, measure comparisons, an analytical expression, facet classification, and a concentration bound linking it to entanglement.