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
本文研究炼金资源理论的反问题，证明在自然假设下，能精确复制并普适编程量子仪器的资源仅允许宇称不对称性和虚数性两种非平凡理论，并揭示精确普适性的全有或全无权衡。
AI 中文摘要
量子资源理论通常以预设的自由结构为起点，并探究在提供某种资源时哪些任务变得可行。我们研究炼金资源理论的反问题，将其定义为允许存在一种既能精确复制自身又能普适地编程量子仪器的资源的资源理论。在自然的一致性假设和分支完备自由性条件下，我们证明对于量子比特单系统，在共同的局域幺正基变换下，仅有两个非平凡理论幸存：宇称不对称性和虚数性。我们进一步证明，精确普适性表现出一种全有或全无的权衡：任何非最大资源态只能精确编程自由幺正操作。这些结果表明，预设的操作能力能强烈约束底层资源结构，并揭示了计算能力与物理实现所需精度之间的基本权衡。
英文摘要
Quantum resource theories usually begin with a prescribed free structure and ask what tasks become possible when a resource is supplied. We study the inverse problem of alchemical resource theories, which we define as resource theories admitting a resource that can both replicate itself exactly and universally simulate quantum instruments. Under natural consistency assumptions and branchwise complete freeness, we show that for multi-qubit systems only two nontrivial theories survive, up to a common local unitary change of basis: parity asymmetry and imaginarity. We further show that exact universality exhibits an all-or-nothing trade-off: any nonmaximal resource state can exactly simulate only free unitaries. These results demonstrate that prescribed operational capabilities can strongly constrain the underlying resource structure and reveal a fundamental trade-off between computational capability and the precision required for physical implementation.
Comments21 pages, 2 figures. Substantially revised manuscript with a significantly improved proof; the assumptions and presentation have also been refined, while the main results remain unchanged
