Pith. sign in

REVIEW 4 cited by

Stabilizer R\'enyi Entropy for Translation-Invariant Matrix Product States

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 2508.03534 v2 pith:T2DBKEV7 submitted 2025-08-05 quant-ph

Stabilizer R\'enyi Entropy for Translation-Invariant Matrix Product States

classification quant-ph
keywords densityentropymagicquantumstabilizerstatesentanglementenyi
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
0 comments
Share X Bluesky LinkedIn Reddit HN
read the original abstract

Magic, capturing the deviation of a quantum state from the stabilizer formalism, is a key resource underpinning the quantum advantage. The recently introduced stabilizer R\'enyi entropy (SRE) offers a tractable measure of magic, avoiding the complexity of conventional methods. We study SRE in translation-invariant matrix product states (MPS), deriving exact expressions for representative states and introducing a numerically stable algorithm, named bond-DMRG, to compute the SRE density in infinite systems. Applying this method, we obtain high-precision SRE densities for the ground state of the one-dimensional Ising model. We also analyze non-local SRE density, showing it is bounded by a universal function of entanglement entropy, and further prove that two-site mutual SRE vanishes asymptotically in injective MPS. Our work not only introduces a powerful method for extracting the SRE density in quantum many-body systems, but also numerically reveals a fundamental connection between magic and entanglement, thereby paving the way for deeper theoretical investigations into their interplay.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 4 Pith papers

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

  1. Stabilizer R\'enyi entropy of 3-uniform hypergraph states

    quant-ph 2026-02 unverdicted novelty 7.0

    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.

  2. Computing quantum magic of state vectors

    quant-ph 2026-01 accept novelty 7.0

    Efficient algorithms compute stabilizer Rényi entropy and mana for quantum states from vectors at O(N d^{2N}) cost using fast Hadamard transform, with open-source implementation.

  3. Spectral signatures of nonstabilizerness and criticality in infinite matrix product states

    quant-ph 2026-02 conditional novelty 6.0

    The stabilizer Rényi entropy of an infinite matrix product state decomposes into bulk, boundary, and exponentially decaying parts, and the associated 'magic correlation length' diverges at criticality with a different...

  4. Limits of Clifford Disentangling in Tensor Network States

    quant-ph 2026-02 conditional novelty 5.0

    Clifford disentangling of tensor-network states works only up to a linear number of T gates; beyond that, magic accumulation defeats it, and a no-go theorem blocks universal single-qubit disentangling.