AI 中文总结
本文建立费米子非高斯性的威廉姆森 majorization 定律，将相关量化指标转化为强单调量，推导态转换条件，且理论可在现有量子设备上验证。
AI 中文摘要
纯态纠缠建立在单一代数基础上：施密特谱的 majorization 支配局域操作和经典通信下的态转换，并约束纠缠单调量。本文针对费米子非高斯性（将自由费米子提升为通用量子计算的资源）建立了相应的 majorization 定律。在任何具有纯态结果的费米子高斯协议下，纯态的 Majorana 协方差矩阵的威廉姆森谱被其系综平均弱 majorized。该谱定律与纠缠理论的谱定律相呼应，将费米子反平坦度、占据熵等可计算的非高斯性量化指标转化为费米子非高斯性的强单调量，并为高斯协议下的态转换提供必要条件和反向界。当费米子宇称守恒时，除非催化剂携带宇称相干性，否则无催化剂能消除 majorization 障碍，且纯态下渐近转换已不可逆。所有相关量均可从两点 Majorana 关联函数获取，使本文发展的理论成为量子物质的实验可观测性质，可在当前量子设备上验证。
英文摘要
Pure-state entanglement rests on a single algebraic backbone: majorization of the Schmidt spectrum governs state conversion under local operations and classical communication, and constrains entanglement monotones. Here we establish a corresponding majorization law for fermionic non-Gaussianity, the resource that elevates free fermions to universal quantum computation. Under any fermionic Gaussian protocol with pure state outcomes, the Williamson spectrum of a pure state's Majorana covariance matrix is weakly majorized by its ensemble average. This spectral law mirrors that of entanglement theory. It turns computable non-Gaussianity quantifiers such as fermionic antiflatness and occupation entropies into strong monotones for fermionic non-Gaussianity, and delivers necessary conditions and converse bounds on state conversion under Gaussian protocols. When fermion parity is conserved, no catalyst can remove a majorization obstruction---unless it carries parity coherence---and asymptotic interconversion is irreversible already for pure states. All relevant quantities are accessible from two-point Majorana correlators, turning the theory developed here into experimentally observable properties of quantum matter, testable on present-day quantum devices.
Comments8+10 pages
