A unified Magic Rényi Entropy measure for spins, bosons, and fermions is shown to have a universal critical contribution determined by the Affleck-Ludwig boundary entropy.
Entanglement and Stabilizer entropies of random bipartite pure quantum states
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abstract
The interplay between non-stabilizerness and entanglement in random states is a very rich arena of study for the understanding of quantum advantage and complexity. In this work, we tackle the problem of such interplay in random pure quantum states. We show that while there is a strong dependence between entanglement and magic, they are, surprisingly, perfectly uncorrelated. We compute the expectation value of non-stabilizerness given the Schmidt spectrum (and thus entanglement). At a first approximation, entanglement determines the average magic on the Schmidt orbit. However, there is a finer structure in the average magic distinguishing different orbits where the flatness of entanglement spectrum is involved.
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quant-ph 5representative citing papers
Maximal stabilizer Rényi entropy for two-qutrit states is ln(81/17), achieved at 18 degenerate maxima; a general prime-d formula ln[d⁴/(2d²−1)] is conjectured and verified for d=2,3,5.
The stabilizer Rényi entropy governs the exponential rate at which Clifford orbits become indistinguishable from Haar-random states and sets the optimal distinguishability from stabilizer states in property testing.
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.
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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Quantum Computational Resources and Conformal Field Theory: Unifying Spins, Bosons, and Fermions
A unified Magic Rényi Entropy measure for spins, bosons, and fermions is shown to have a universal critical contribution determined by the Affleck-Ludwig boundary entropy.
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Analytical Landscape of Maximal Magic for Two-Qutrit States and Beyond
Maximal stabilizer Rényi entropy for two-qutrit states is ln(81/17), achieved at 18 degenerate maxima; a general prime-d formula ln[d⁴/(2d²−1)] is conjectured and verified for d=2,3,5.
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Operational interpretation of the Stabilizer Entropy
The stabilizer Rényi entropy governs the exponential rate at which Clifford orbits become indistinguishable from Haar-random states and sets the optimal distinguishability from stabilizer states in property testing.
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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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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.