发表机构
The Hong Kong University of Science and Technology (Guangzhou); Quantum Science Center of Guangdong–Hong Kong–Macao Greater Bay Area（香港科技大学（广州）; 粤港澳大湾区量子科学中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究加权泡利控制下多副本量子态制备，证明其成本严格非可加，四脉冲集体协议制备两个T态更优，并揭示集体节省机制与熵速度极限。
AI 中文摘要
量子态制备是量子计算与控制的基本原语，但其资源成本通常针对单个目标态或在独立副本构造下进行分析。这里我们研究加权泡利控制下的多副本问题，其中泡利乘积旋转 $e^{i\phi P}$ 按其旋转角 $|\phi|$ 计费，与 $P$ 的权重无关。我们推导了精确的单量子比特制备成本，并证明其严格非可加：一个四脉冲集体协议以低于两个最优单副本协议的成本制备两个 $T$ 态。我们进一步识别了布洛赫球上具有集体节省的有限区域，包括始终保持乘积态的轨迹，表明瞬态纠缠并非优势背后的唯一机制。补充地，一个与维度无关的 Rényi 熵速度极限为每个相干目标给出了广泛下界，并在低于有限制备速率时给出指数保真度惩罚。这些结果建立了态合成的多副本几何，其中不相关的输出仍可从集体控制中受益。
英文摘要
Quantum state preparation is a basic primitive of quantum computation and control, but its resource cost is usually analyzed for one target state or under an independent-copy construction. Here we study the many-copy problem under weighted Pauli control, where a Pauli-product rotation $e^{iϕP}$ is charged by its rotation angle $|ϕ|$, independently of the weight of $P$. We derive the exact single-qubit preparation cost and show that it is strictly nonadditive: a four-pulse collective protocol prepares two $T$ states at lower cost than two optimal one-copy protocols. We further identify finite regions of the Bloch sphere with collective saving, including trajectories that remain product throughout, showing that transient entanglement is not the only mechanism behind the advantage. Complementarily, a dimension-independent Rényi-entropy speed limit gives an extensive lower bound for every coherent target and an exponential fidelity penalty below a finite preparation rate. These results establish a many-copy geometry of state synthesis in which uncorrelated outputs can nevertheless benefit from collective control.
Comments5+15 pages
