发表机构
Changchun University of Technology; Yanbian University; Capital Normal University; Max-Planck-Institute for Mathematics in the Sciences（长春工业大学; 延边大学; 首都师范大学; 马克斯·普朗克科学促进部数理研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究定义了酉可达相干擦除距离，推导了量子比特的精确解和非简并量子三能级系统的紧致普适界，该距离还对应有界酉驱动下的最小相干擦除时间，具有操作意义。
AI 中文摘要
我们引入酉可达相干擦除距离，该距离用于衡量将量子态变换为无相干态且不改变其谱所需的最小酉控制代价。目标态被限制在同一酉轨道上的无相干态，这导致其几何结构不同于传统的态空间邻近性。我们建立了与轨道受限量子传输、Bures几何及酉控制距离相关的不等式。这些量在纯态下一致，但在混合态下可能不同。对于量子比特，我们推导了精确表达式，并表明在非简并情形下，相干擦除代价依赖于本征基取向而非本征值。对于非简并量子三能级系统，我们将问题简化为单项式酉群上的优化问题，推导得到紧致普适界arccos[(2√2-1)/4]，并构造了达到该界的显式本征基。所得距离还确定了有界酉驱动下的最小相干擦除时间，赋予其直接的操作意义。
英文摘要
We introduce the unitary-accessible coherence-erasure distance, which measures the minimum unitary-control cost required to transform a quantum state into an incoherent state without changing its spectrum. The target states are restricted to incoherent states on the same unitary orbit, leading to a geometry different from conventional state-space proximity. We establish inequalities relating orbit-restricted quantum transport, Bures geometry, and the unitary-control distance. These quantities coincide for pure states but can differ for mixed states. For qubits, we derive an exact expression and show that, in the nondegenerate case, the coherence-erasure cost depends on the eigenbasis orientation rather than on the eigenvalues. For nondegenerate qutrits, we reduce the problem to an optimization over the monomial unitary group. We derive the tight universal bound $\arccos[(2\sqrt2-1)/4]$ and construct an explicit eigenbasis that attains it. The resulting distance also determines the minimum coherence-erasure time under bounded unitary driving, giving it a direct operational meaning.
Comments20 pages, 4 figures,
