发表机构
Rubin Anders Scientific, Inc.（鲁宾安德斯科学有限公司）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明混合费米子及真空附近玻色子高斯态的单副本层析下界为Ω(m³/ε²)，与集体测量Θ(m²/ε²)分离，并给出双模纠缠优势的数值见证。
AI 中文摘要
我们证明，当测量每次仅作用于一个副本时，学习 $m$ 模上未知混合费米子高斯态至迹距离 $\epsilon$ 需要 $\Omega(m^3/\epsilon^2)$ 个副本，即使允许任意 POVM、新鲜辅助比特和经典自适应，但在副本之间没有量子内存。该下界适用于 $0<\epsilon\le1/3600$，并将此模型与已知的集体速率 $\Theta(m^2/\epsilon^2)$ 区分开来。它源于统一的单副本 Fisher 信息预算以及迹距离与高斯参数之间的维度无关比较。在算子范数至多 $1-c$ 的协方差矩阵上，我们证明了 Frobenius 到迹范数的连续性界，常数为 $[2c(2-c)]^{-1/2}$；matchgate 阴影随后达到 $O(m^3/(c\epsilon^2))$ 个副本。这也为热自由费米子态提供了显式误差证书。对于总平均光子数至多为一的一类混合被动玻色子高斯态，归约到有界块 qudit 层析给出了单副本下界 $\Omega(m^3/(\epsilon^2\sqrt{\log(m/\epsilon)}))$，而集体复杂度为 $\Theta(m^2/\epsilon^2)$。这些分离回答了 Chen 等人提出的混合态测量资源问题。一个双模例子具有最优两副本 Fisher 迹 $5$，而可分上限为 $4$。IBM 复制实验给出了预注册的见证下界 $4.12$，单侧 $95\\%$ 散粒噪声置信度；其解释假设了规定的制备和共同的测量通道，并且不约束制备系统误差。
英文摘要
We prove that learning an unknown mixed fermionic Gaussian state on $m$ modes to trace distance $ε$ requires $Ω(m^3/ε^2)$ copies when measurements act on one copy at a time, even with arbitrary POVMs, fresh ancillas and classical adaptivity, but without quantum memory between copies. The bound holds for $0<ε\le1/3600$ and separates this model from the known collective rate $Θ(m^2/ε^2)$. It follows from a uniform single-copy Fisher-information budget and a dimension-independent comparison between trace distance and Gaussian parameters. On covariance matrices of operator norm at most $1-c$, we prove a Frobenius-to-trace-norm continuity bound with constant $[2c(2-c)]^{-1/2}$; matchgate shadows then attain $O(m^3/(cε^2))$ copies. This also gives explicit error certificates for thermal free-fermion states. For a class of mixed passive bosonic Gaussian states with total mean photon number at most one, a reduction to bounded-block qudit tomography gives a single-copy lower bound $Ω(m^3/(ε^2\sqrt{\log(m/ε)}))$, versus collective complexity $Θ(m^2/ε^2)$. These separations answer the mixed-state measurement-resource question posed by Chen et al. A two-mode example has optimal two-copy Fisher trace $5$, versus the separable ceiling $4$. An IBM replication gave a pre-registered witness lower bound $4.12$ at one-sided $95\%$ shot-noise confidence; its interpretation assumes the prescribed preparations and a common measurement channel and does not bound preparation systematics.
Comments38 pages, 1 figure. Ancillary files: IBM pilot and replication data, circuits, and offline recount code
