发表机构
International Centre for Theory of Quantum Technologies, University of Gdańsk（格但斯克大学量子理论国际中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究针对正交群轨道上的纯态，确定了非对称量子克隆的完整可达保真度区域，构造了最优克隆通道，并应用于四模费米子态，发现局部最优克隆器唯一且无法用保高斯操作实现。
AI 中文摘要
在这项工作中，我们研究了属于正交群生成的轨道上的纯态的非对称（1到2）量子克隆。对于每个维度（d≥3），我们确定了平均单副本保真度的可达对的完整区域。利用正交协变性和Brauer代数，我们将对所有CPTP映射的优化简化为有限维谱问题，并构造了显式的最优克隆通道。然后，我们将一般结果应用于偶宇称扇区中的四模费米子态。利用三元性，我们将固定并发度的费米子族与论文第一部分中考虑的正交轨道等同起来。特别地，对于纯高斯态，我们证明了对称局部最优克隆器是唯一的。我们还比较了局部克隆和全局克隆，发现对于联合双副本保真度最优的通道与对于单副本保真度最优的通道不同。最后，我们证明了局部最优克隆器不能仅使用保持费米子高斯态的操作来实现。
英文摘要
In this work, we study asymmetric $(1\to2)$ quantum cloning for pure states belonging to orbits generated by the orthogonal group. For every dimension $(d\geq3)$, we determine the full region of achievable pairs of average single-copy fidelities. Using orthogonal covariance and the Brauer algebra, we reduce the optimization over all CPTP maps to a finite-dimensional spectral problem and construct explicit optimal cloning channels. We then apply the general results to four-mode fermionic states in the even-parity sector. Using triality, we identify the fixed-concurrence fermionic families with the orthogonal orbits considered in the first part of the paper. In particular, for pure Gaussian states we show that the symmetric locally optimal cloner is unique. We also compare local and global cloning and find that the channel optimal for the joint two-copy fidelity is different from the one optimal for the single-copy fidelities. Finally, we show that the locally optimal cloner cannot be implemented using only operations which preserve fermionic Gaussian states.
Comments19 pages, 5 figures, comments welcome
