发表机构
University of Cambridge; University of Gdańsk; University of Oxford（剑桥大学; 格但斯克大学; 牛津大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究费米子高斯态，证明高斯德·菲内蒂定理指数变体，给出原始态与其近似值误差界，改进维度惩罚，扩展到高斯不变态类，表明其与高斯对称态关系及可纯化，将德·菲内蒂定理扩展到该态集。
AI 中文摘要
我们证明了高斯德·菲内蒂定理的指数变体：置换不变的自由费米子高斯态的子系统可以由几乎独立同分布状态的凸组合很好地近似，这些状态在其部分子集上是高斯的。我们的结果给出了原始状态与其近似值之间的误差界，该误差界在无约束部分的数量上呈指数衰减，当所考虑的子系统较小时变为超指数衰减。我们的界的维度惩罚在局部希尔伯特空间维度上是多对数的，比[《自然物理学》3, 645 - 649]中的标准德·菲内蒂定理有指数级改进。在完全独立同分布的极限下，我们的界恢复了[arXiv:2603.12392]中的高斯德·菲内蒂定理。先前的工作考虑了高斯对称态，我们将其扩展到更广泛的高斯不变态类，包括例如单副本混合高斯态的独立同分布副本。我们表明高斯不变态恰好是局部放大副本上高斯对称态的部分迹，并且总是允许纯化到更大的高斯对称态。这将德·菲内蒂定理扩展到了整个高斯不变态集，误差界的维度惩罚仅增加了多项式。
英文摘要
We prove an exponential variant of the Gaussian de Finetti theorem: the subsystems of permutation-invariant, free-fermionic Gaussian states are well approximated by convex combinations of almost-i.i.d. states that are Gaussian on subsets of their parts. Our result provides an error bound between the original state and its approximants that decays exponentially in the number of unconstrained parts, becoming super-exponential when the subsystem under consideration is small. The dependence of our bound on the local Hilbert space dimension is polylogarithmic, giving an exponential improvement over the standard de Finetti theorem of [Nat. Phys. 3, 645-649]. Previous works considered Gaussian-symmetric states, which are supported on the trivial irrep of the tensor matchgate representation. We extend these results to the broader class of Gaussian-invariant states, which contains, for example, i.i.d. copies of single-replica mixed Gaussian states. We show that Gaussian-invariant states are precisely the partial traces of Gaussian-symmetric states on locally enlarged replicas and always admit a purification into a larger Gaussian-symmetric state. As an application, we derive explicit convergence bounds for a hierarchy of convex relaxations of polynomial optimisation over fermionic Gaussian states. For variational energy minimisation, the hierarchy gives lower bounds converging to the global Gaussian minimum. Combined with upper bounds from Gaussian trial states, these bounds quantify how far a variational calculation can be from the best energy attainable within the Gaussian family.
Comments7+23 pages, 1 figure; v2 contains applications to optimisation over Fermionic Gaussian states
