AI 中文总结
研究通过引入魔法雷尼熵统一量化自旋、玻色子和费米子的计算资源，用共形场论分析揭示临界多体状态中非稳定性和非高斯性的普遍方面及关系，还通过具体例子和数值计算验证。
AI 中文摘要
通过量子资源视角表征量子态为多体系统提供信息论观点。量子魔法可捕捉多体状态中与纠缠互补的方面。本文引入魔法雷尼熵统一量化自旋、玻色子和费米子的计算资源，揭示临界多体状态中非稳定性和非高斯性的普遍方面，通过具体例子和数值计算验证，提供多体魔法的统一场论理解。
英文摘要
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, captures 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 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. We show that the MRE is a resource monotone under stabilizer and Gaussian protocols involving measurements and feedforward operations. The MRE reveals 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 transition through bulk-induced boundary renormalization-group flows. As a concrete example, we present a 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 $K=3$. Our field-theoretical predictions are confirmed by numerical calculations. These results provide a unified field-theoretical understanding of many-body magic across spins, bosons, and fermions.
CommentsProofs of monotonicity for MRE and strong monotonicity for linear MRE under bosonic and fermionic Gaussian protocols have been added
