发表机构
Institute for Advanced Studies in Basic Sciences; Ferdowsi University of Mashhad（基础科学高级研究院; 马什哈德菲尔多西大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明一般二次演化下结构费米子态可被高效重构，利用高斯测量和四阶关联识别隐藏块，实现多项式资源下的保真度保证。
AI 中文摘要
我们证明，由不相交分支的固定粒子数块制备的未知纯费米子态，在经历一般二次演化（包括粒子对的产生与湮灭）后可以被重构。对于每个块的固定粒子数上限，自适应或非自适应的单副本高斯测量能够以规定的保真度和置信度，利用系统规模和逆保真度的多项式资源，获得经典输入和电路描述。自适应过程具有更优的副本保证。连通四阶关联和协方差相容的交换子识别隐藏块；局部状态通过新测量或预定的有界度矩表恢复。稳定的分支恢复给出有效的制备描述。既不需要粒子数守恒，也不要求块均匀性；不假设分支权重或协方差间隙的下界。一个认证变体在承诺族内存在被动制备时返回被动制备，无需预先的成员信息。在配对魔态的完整高斯轨道上，仅四阶测量就足够，并有一个显式界限将观测误差转换为状态误差。
英文摘要
We prove that unknown pure fermionic states prepared from disjoint-branch fixed-particle-number blocks can be reconstructed after general quadratic evolution, including pair creation and annihilation. For a fixed particle cap per block, adaptive or nonadaptive single-copy Gaussian measurements yield classical input and circuit descriptions with prescribed fidelity and confidence, using polynomial resources in system size and inverse infidelity. The adaptive procedure has the sharper copy guarantee. Connected quartic correlations and a covariance-compatible commutant identify the hidden blocks; local states are recovered from fresh measurements or a predetermined bounded-degree moment table. Stable branch recovery gives valid preparation descriptions. Neither particle-number conservation nor block homogeneity is required; no lower bound on branch weights or covariance gaps is assumed. A certified variant returns a passive preparation whenever one exists within the promised family, without advance membership information. On the full Gaussian orbit of paired magic states, quartic measurements alone suffice, with an explicit bound converting observable error into state error.
Comments46 pages, 3 figures; supporting Lean files included as ancillary material
