发表机构
NTT Communication Science Laboratories, NTT, Inc.（NTT通信科学实验室，日本电信电话株式会社）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该论文提出四元数性资源理论，证明每个纯态均可作为可复制资源，实现任意量子操作的精确模拟，并优于现有方法。
AI 中文摘要
一种炼金资源理论允许存在一个非自由态，该态可以通过自由操作被精确复制，并且其有限个副本能够精确模拟任意量子仪器。目前已知的唯一非平凡例子是虚数性和奇偶不对称性，它们穷尽了量子比特情形（arXiv:2609.12988），并表现出全有或全无的性质：任何非最大资源只能精确模拟自由酉操作。我们针对偶数维量子比特$d\ge4$引入了四元数性，其基础是由反酉算子$\Theta$（满足$\Theta^2=-I$）表示的四元数结构。它在两种意义上都是极端的：每个纯态都是炼金的，并且炼金性在混合下最大程度地丰富。在此框架内，对于任何非平凡的$d$维资源理论和纯炼金态$g$，允许的纯混合集满足$\dim\mathcal M_g\le 2d-4$，而四元数性对每个纯态都饱和了这一界限。反之，这两个极端性质刻画了四元数结构。由于每个纯态都是炼金的，初始资源可以选择与已知噪声结构相匹配。此外，当噪声资源态保持在共同的迷向子空间内时，相同的自由处理器可以精确地处理所有资源态，同时保持资源不变。这实现了无需重新校准的精确模拟，包括通用量子计算，并已在标准退相位和耗散噪声中实现，其中四元数性显著优于虚数性和奇偶不对称性。
英文摘要
An alchemical resource theory admits a nonfree state that can be exactly replicated by free operations and whose finitely many copies enable exact simulation of arbitrary quantum instruments. The only known nontrivial examples, imaginarity and parity asymmetry, exhaust the qubit case (arXiv:2609.12988) and exhibit an all-or-nothing property: any nonmaximal resource exactly simulates only free unitaries. We introduce aquaternionicity for even-dimensional qudits $d\ge4$, based on a quaternionic structure represented by an antiunitary $Θ$ with $Θ^2=-I$. It is extremal in two senses: every pure state is alchemical, and alchemicality is maximally abundant under mixing. Within this framework, for any nontrivial $d$-dimensional resource theory and pure alchemical state $g$, the admissible pure-mixing set satisfies $\dim\mathcal M_g\le 2d-4,$ which aquaternionicity saturates for every pure state. Conversely, these two extremal properties characterize the quaternionic structure. Because every pure state is alchemical, the initial resource can be chosen to match the known noise structure. Moreover, when the noisy resource states remain within a common isotropic subspace, the same free processor works exactly for all of them while returning the resource unchanged. This enables recalibration-free exact simulation, including universal quantum computation, and is realized for standard dephasing and dissipative noise, where aquaternionicity substantially outperforms imaginarity and parity asymmetry.
Comments37pages, 1figure
