发表机构
University of Helsinki; the Finnish Quantum Institute; Helsinki Institute of Physics（赫尔辛基大学; 芬兰量子研究所; 赫尔辛基物理研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究反平坦性的资源理论中保平坦度操作（FPOs）的识别问题，明确FPOs的两类形式及平坦态凸组合的规则，解决了该领域的一个开放问题。
AI 中文摘要
量子态若与投影算子成比例则称为平坦态。近来人们对反平坦性（即偏离平坦态的性质）的研究及建立其资源理论产生了兴趣，而识别自由操作（即保平坦度操作（FPOs））仍是一个未解决的问题。为此，我们首先讨论保正交性操作（OPOs），孤立系统中的幺正操作是其平凡例子。更一般地，我们给出一个简单证明，所有OPOs都是由幺正操作/等距变换与附加固定态组合构成的等距嵌入。随后我们证明，所有FPOs要么是映射到某个固定平坦态的常值映射，要么是OPO的特例，其中附加的固定态必须是平坦态。我们还证明，平坦态的唯一可能的凸组合是正交平坦态的凸组合，其权重由它们的纯度给出。
英文摘要
A quantum state is called flat if it is proportional to a projector. There has been recent interest in studying antiflatness, the property of diverging from flat states, and establishing a resource theory for it. Identifying the free operations (the Flatness-Preserving Operations (FPOs)) remained an open problem. For this purpose, we first discuss Orthogonality-Preserving Operations (OPOs), of which trivial examples are unitary operations in an isolated system. More generally, we give a simple proof that all OPOs are isometric embeddings consisting of combinations of unitaries/isometries and appending a fixed state. We then show that all FPOs are either constant maps to some fixed flat state or a special case of an OPO, where the appended fixed state must be a flat state. We also show that the only possible flat convex combinations of flat states are those of orthogonal flat states with weights given by their purities.
