Stabilizer R\'{e}nyi Entropy Encodes Fusion Rules of Topological Defects and Boundaries

TL;DR

This paper shows that the stabilizer Rényi entropy can detect universal properties of conformal defects and boundaries in quantum critical systems, reflecting fusion rules and noninvertible symmetries.

Contribution

It introduces the use of stabilizer Rényi entropy as an information-theoretic probe for topological defects and boundaries in conformal field theories, supported by analytical and numerical evidence.

Findings

Boundaries produce a universal logarithmic correction to SRE.

Topological defects yield a universal size-independent term in SRE.

Universal terms in SRE reflect defect-fusion rules and noninvertible symmetry algebra.

Abstract

We demonstrate that the stabilizer R\'{e}nyi entropy (SRE), a computable measure of quantum magic, can serve as an information-theoretic probe for universal properties associated with conformal defects in one-dimensional quantum critical systems. Using boundary conformal field theory, we show that open boundaries manifest as a universal logarithmic correction to the SRE, whereas topological defects yield a universal size-independent term. When multiple defects are present, we find that the universal terms in the SRE faithfully reflect the defect-fusion rules that define a noninvertible symmetry algebra. These analytical predictions are corroborated by numerical calculations of the Ising model, where boundaries and topological defects are described by Cardy states and Verlinde lines, respectively.