Curator's Take
This article introduces a single “magic Rényi entropy” that quantifies both non‑stabilizerness in spin models and non‑Gaussianity in bosonic and fermionic systems, giving researchers a common language to compare computational resources across very different many‑body platforms. By showing that the size‑independent term of this measure is set by the Affleck‑Ludwig boundary entropy—and can be tuned or even trigger boundary phase transitions—the work links universal CFT data directly to the power needed for universal quantum computation. The result opens a pathway to diagnose and engineer critical states with optimal computational usefulness, a step toward more resource‑aware quantum simulators and error‑resilient architectures.
— Mark Eatherly
Summary
Characterizing a quantum state through the lens of quantum resources provides an information-theoretic perspective on many-body systems. While quantum entanglement serves as the paradigmatic example of a quantum resource, recent studies have shown that quantum magic, a resource for universal quantum computation, can capture aspects of many-body states complementary to those described by entanglement. For instance, in spin systems, conformal field theory (CFT) analysis of the stabilizer Rényi entropy has revealed universal features of nonstabilizerness that are qualitatively distinct from entanglement. In bosonic and fermionic systems, however, a comparable formulation for their computational resource, non-Gaussianity, has yet to be established. In this work, we introduce a unified measure, the magic Rényi entropy (MRE), to quantify computational resources in spins, bosons, and fermions on an equal footing. This allows us to reveal common universal aspects of nonstabilizerness and non-Gaussianity in critical many-body states. In particular, our CFT analysis shows that the universal contribution to the MRE appears as the size-independent term determined by the Affleck-Ludwig boundary entropy. We find that non-Gaussianity can continuously renormalize this universal contribution or drive a boundary phase transition through bulk-induced boundary renormalization-group flows. As a concrete demonstration, we present a detailed CFT analysis of non-Gaussianity in interacting spinless fermions described by the Tomonaga-Luttinger liquid, showing boundary transitions at the Luttinger parameters $K=1/3$ and $K=3$. We perform numerical calculations that confirm our field-theoretical predictions. These results provide a unified field-theoretical understanding of many-body magic across spins, bosons, and fermions.