发表机构
The University of Tokyo（东京大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究推导了费米子非高斯性的普适上界，并发现Sachdev-Ye-Kitaev哈密顿量演化下MRE密度出现一阶相变，伴随置换对称性自发破缺。
AI 中文摘要
费米子非高斯性是通用量子计算的一种资源，可通过量子多体系统中的相互作用产生。我们以魔幻Rényi熵（MRE）作为非高斯性的度量，推导了其普适上界和Haar平均值，证明在大系统极限下，典型的Haar随机态每个马约拉纳算符达到最大MRE密度$\ln(4/3)$。我们还表明，具有相同协方差矩阵的态之间，MRE可以存在广延差异。为了研究非高斯性如何增长至这一最大密度，我们在Sachdev-Ye-Kitaev哈密顿量下对高斯态进行虚时和实时演化。通过改变虚时和实时的持续时间，我们识别出一阶相变，其特征是MRE密度出现扭结，以及用于评估MRE的四个副本之间的置换对称性自发破缺。这一相变代表了态非高斯性的定性变化，而这种变化并未反映在热自由能中。
英文摘要
Fermionic non-Gaussianity is a resource for universal quantum computation that can be generated by interactions in quantum many-body systems. Using the magic Rényi entropy (MRE) as a measure of non-Gaussianity, we derive its universal upper bound and Haar mean, proving that typical Haar-random states attain the maximal MRE density of $\ln(4/3)$ per Majorana in the large-system limit. We also show that the MRE can differ extensively between states with identical covariance matrices. To investigate how non-Gaussianity grows toward this maximal density, we evolve a Gaussian state in imaginary and real time under the Sachdev-Ye-Kitaev Hamiltonian. By varying the imaginary- and real-time durations, we identify a first-order transition marked by a kink in the MRE density and spontaneous breaking of the permutation symmetry among the four copies used to evaluate the MRE. This transition represents a qualitative change in the non-Gaussianity of the state that is not reflected in the thermal free energy.
Comments33 pages, 2 figures
