Pith. sign in

REVIEW 8 cited by

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

Not yet reviewed by Pith; the record is open.

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2501.12146 v3 pith:F7WXI6BM submitted 2025-01-21 quant-ph cond-mat.str-elphysics.comp-phphysics.data-an

classification quant-phcond-mat.str-elphysics.comp-phphysics.data-an
keywords magicalphacriticalemphmany-bodypointsreducedentropy
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
abstract

We present a novel quantum Monte Carlo method for evaluating the $\alpha$-stabilizer R\'enyi entropy (SRE) for any integer $\alpha\ge 2$. By interpreting $\alpha$-SRE as partition function ratios, we eliminate the sign problem in the imaginary-time path integral by sampling \emph{reduced Pauli strings} within a \emph{reduced configuration space}, which enables efficient classical computations of $\alpha$-SRE and its derivatives to explore magic in previously inaccessible 2D/higher-dimensional systems. We first isolate the free energy part in $2$-SRE, which is a trivial term. Notably, at quantum critical points in 1D/2D transverse field Ising (TFI) models, we reveal nontrivial singularities associated with the \emph{characteristic function} contribution, directly tied to magic. Their interplay leads to complicated behaviors of $2$-SRE, avoiding extrema at critical points generally. In contrast, analyzing the volume-law correction to SRE reveals a discontinuity tied to criticalities, suggesting that it is more informative than the full-state magic. For conformal critical points, we claim it could reflect nonlocal magic residing in correlations. Finally, we verify that $2$-SRE fails to characterize magic in mixed states (e.g. Gibbs states), yielding nonphysical results. This work provides a powerful tool for exploring the roles of magic in large-scale many-body systems, and reveals intrinsic relation between magic and many-body physics.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 8 Pith papers

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

  1. Universality of Magic in Local Quantum Field Theory

    hep-th 2026-07 conditional novelty 7.0 of 10

    In any local QFT, vacuum-like states have non-flat entanglement spectra because local algebras are type III₁, so no stabilizer state can flow to them in the continuum: QFT states necessarily carry magic.

  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. Pauli Spectrum and Stabilizer R\'enyi Entropy in Gapless Symmetry-Protected Topological Phases

    cond-mat.str-el 2026-07 conditional novelty 6.0 of 10

    Stabilizer Rényi entropy signals SPT transitions via extrema, but Pauli-spectrum crossings of string-order operators distinguish the phases via local-unitary or non-invertible dualities.

  5. Universal Spreading of Nonstabilizerness and Quantum Transport

    quant-ph 2025-06 conditional novelty 6.0 of 10

    In the XXZ chain after a domain-wall quench, both stabilizer Rényi entropy and participation entropy grow as t^{1/z} with z the ballistic (1), diffusive (2), or KPZ (3/2) transport exponent.

  6. Computing Quantum Resources using Tensor Cross Interpolation

    quant-ph 2025-02 conditional novelty 6.0 of 10

    A tensor cross interpolation method computes quantum resource quantifiers directly from their definitions, demonstrated for stabilizer Rényi entropy in 1D and relative entropy of coherence in 2D Ising models.

  7. Quantum Non-Local Nonstabilizerness

    quant-ph 2025-02 conditional novelty 6.0 of 10

    Non-local nonstabilizerness is exactly computable for two-qubit pure states and shows power-law scaling and a measurement-induced 'nonstabilizerness swapping' effect in critical systems.

  8. Nonstabilizerness in the unitary and monitored quantum dynamics of XXZ-staggered and SYK models

    quant-ph 2025-02 conditional novelty 6.0 of 10

    In monitored quantum-state-diffusion dynamics of XX, XXZ-staggered and SYK models, the steady-state nonstabilizerness is fit by a generalized Lorentzian and grows linearly with system size with no measurement-induced ...

Pith tools