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
Stabilizer R\'enyi Entropy for Translation-Invariant Matrix Product States
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.
Forward citations
Cited by 4 Pith papers
-
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.
-
Computing quantum magic of state vectors
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.
-
Spectral signatures of nonstabilizerness and criticality in infinite matrix product states
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...
-
Limits of Clifford Disentangling in Tensor Network States
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.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.