论文标题
不对称量子克隆区域
The Asymmetric Quantum Cloning Region
论文作者
论文摘要
量子克隆是量子信息理论的基本协议。量子力学定律禁止完美的通用量子克隆，只有不完美的副本才能达到。当克隆质量相同时，对称量子克隆与情况有关。在这项工作中，我们研究了$ 1 \至n $非对称克隆的一般情况，有人要求克隆的任意品质。我们表征了所有希尔伯特空间维度和克隆数量，这是所有可能的克隆品质的集合。该集合被实现为新引入规范的单位球的非负部分，我们称之为$ \ Mathcal {q} $ - norm-Norm。我们还为实现给定克隆质量矢量的量子克隆器提供了封闭形式的表达式。我们的分析依赖于Schur-Weyl二元性以及对部分转移置换式运算符的光谱特性的研究。
Quantum cloning is a fundamental protocol of quantum information theory. Perfect universal quantum cloning is prohibited by the laws of quantum mechanics, only imperfect copies being reachable. Symmetric quantum cloning is concerned with case when the quality of the clones is identical. In this work, we study the general case of $1 \to N$ asymmetric cloning, where one asks for arbitrary qualities of the clones. We characterize, for all Hilbert space dimensions and number of clones, the set of all possible clone qualities. This set is realized as the nonnegative part of the unit ball of a newly introduced norm, which we call the $\mathcal{Q}$-norm. We also provide a closed form expression for the quantum cloner achieving a given clone quality vector. Our analysis relies on the Schur-Weyl duality and on the study of the spectral properties of partially transposed permutation operators.
