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Pauli Spectrum and Non-stabilizerness of Typical Quantum Many-Body States

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arxiv 2312.11631 v2 pith:RPRGIR7O submitted 2023-12-18 quant-ph cond-mat.stat-mechhep-th

Xhek Turkeshi , Anatoly Dymarsky , Piotr Sierant This is my paper · ORCID
classification quant-phcond-mat.stat-mechhep-th
keywords statesquantumpaulispectrumtypicalrandomatypicalhaar
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An important question of quantum information is to characterize genuinely quantum (beyond-Clifford) resources necessary for universal quantum computing. Here, we use the Pauli spectrum to quantify how magic, beyond Clifford, typical many-qubit states are. We first present a phenomenological picture of the Pauli spectrum based on quantum typicality and then confirm it for Haar random states. We then introduce filtered stabilizer entropy, a magic measure that can resolve the difference between typical and atypical states. We proceed with the numerical study of the Pauli spectrum of states created by random circuits as well as for eigenstates of chaotic Hamiltonians. We find that in both cases the Pauli spectrum approaches the one of Haar random states, up to exponentially suppressed tails. Our results underscore differences between typical and atypical states from the point of view of quantum information.

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Cited by 6 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Evaluating many-body stabilizer R\'enyi entropy by sampling reduced Pauli strings: singularities, volume law, and nonlocal magic

    quant-ph 2025-01 conditional novelty 8.0 of 10

    A sign-problem-free quantum Monte Carlo algorithm computes stabilizer Rényi entropy derivatives, revealing critical-point singularities and volume-law corrections that show discontinuity across phase transitions.

  2. Magic without a phase: phase-independent stabilizer R\'enyi entropy in gluon scattering

    hep-th 2026-07 conditional novelty 7.0 of 10

    A phase-averaged stabilizer Rényi entropy is introduced for tree-level gluon scattering, with color-independent phase-independent magic that is larger in 3→2 than 2→2 and has a soft-limit lower bound in 2→3.

  3. Connecting Magic Dynamics in Thermofield Double States to Spectral Form Factors

    quant-ph 2026-01 conditional novelty 7.0 of 10

    For chaotic all-to-all systems, the stabilizer Rényi entropy of thermofield double states is set by the spectral form factor and saturates through a first-order dynamical transition.

  4. Quantum detection of CP violation in the $t\bar{t}$ system: production

    hep-ph 2026-07 conditional novelty 6.0 of 10

    CP-odd SMEFT top interactions appear as ΔB and antisymmetric C_A in the tt̄ production density matrix; direct markers beat most QI measures for CP sensitivity at LHC and FCC-ee.

  5. On the stabilizer complexity of Hawking radiation

    hep-th 2025-10 conditional novelty 6.0 of 10

    In the PSSY model, the Wigner negativity (stabilizer magic) of Hawking radiation is O(1) before the Page time and grows as sqrt(2/pi) exp((S_max - S_2)/2) afterward; a similar formula is proposed for holographic state...

  6. Spin versus Magic: Lessons from Gluon and Graviton Scattering

    hep-th 2025-08 accept novelty 6.0 of 10

    For 2 to 2 scattering of massless spin-1/2 to spin-2 particles, the averaged generated magic decreases monotonically with spin, with maxima well below the two-qubit upper bound.

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