AI 中文总结
该研究确定了秩至多为r的d维量子态的最优渐近复制复杂度，给出了输入拷贝数的渐近标度关系，并揭示了克隆与层析复杂度的操作关联。
AI 中文摘要
量子态克隆是从有限数量的输入拷贝中近似制备未知量子态的额外拷贝的任务。纯态的最优克隆保真度已被精确知晓，但一般混合态尚无类似的刻画。我们确定了秩至多为r的d维态的最优渐近复制复杂度：以最坏情况保真度至少1-ε制备M个额外拷贝，需要且可通过N=Θ(Mrd/ε)个输入拷贝实现。值得注意的是，下界已对具有固定平坦谱的一类态成立，而匹配的上界可通过随机纯化后接最优纯态克隆实现。当M=1时，我们进一步证明，高保真度量子态层析可被相干转换为具有相当误差的克隆，揭示了匹配的克隆与层析复杂度的操作起源。
英文摘要
Quantum state cloning is the task of approximately producing additional copies of an unknown quantum state from a finite number of input copies. The optimal cloning fidelity is known exactly for pure states, but no comparable characterization is known for general mixed states. We determine the optimal asymptotic copy complexity for $d$-dimensional states of rank at most $r$: producing $M$ additional copies with worst-case fidelity at least $1-\varepsilon$ requires and is achievable with $N=Θ(Mrd/\varepsilon)$ input copies. Remarkably, the lower bound already holds for a family of states with a fixed flat spectrum, while the matching upper bound is achieved by random purification followed by optimal pure-state cloning. For $M=1$, we further show that high-fidelity tomography can be coherently converted into cloning with comparable error, revealing an operational origin of the matching cloning and tomography complexities.
Comments28 pages, 6 figures
