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arXiv 2509.08059quant-ph
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克隆量子信道

Cloning Quantum Channels

Pavel Sekatski, Yelena Guryanova, Naga Bhavya Teja Kothakonda, Michalis Skotiniotis

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18+15 pages
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AI总结：

该论文构建统一框架研究量子信道的最优克隆，证明态克隆为特例，给出超复制的必要条件，并发现噪声相位门信道满足条件，而酉门等不满足，还提出SDP算法并建立与贝叶斯估计的联系。

摘要：

我们考虑以最佳可达速率和最高质量确定性克隆量子信道的问题，即所谓的最优克隆。我们证明克隆量子态实际上等价于克隆“丢弃并替换”信道，因此前者是更一般问题的一个特例。通过诉诸高阶量子操作（量子过程），我们构建了一个统一框架来处理最一般的克隆任务，并为信道族表现出超复制（一种具有消失误差的二次克隆速率）建立了必要条件。我们发现噪声相位门信道满足这些条件，并为该任务构造了显式的超复制过程。相反，我们发现这些标准不适用于全部噪声酉门集合、经典噪声信道或振幅阻尼信道，它们各自的克隆速率至多是线性的。在这一范式中，我们不仅推导出新结果，还重新诠释了已知结果。我们推导了态克隆的强逆定理，对于酉信道，我们构造了一种基于测量-制备过程的替代超复制过程，不同于Dür等人[PRL 114, 120503 (2015)]和Chiribella等人[PRL 114, 120504 (2015)]的结果，这使我们能够建立最优信道克隆与贝叶斯信道估计之间的直接联系。最后，我们给出一个SDP算法来搜索最优克隆过程，并在具体实例上研究相干协议与测量-制备协议的优势。

英文摘要：

We consider the problem of deterministically cloning quantum channels with respect to the best attainable rate and the highest quality, so-called optimal cloning. We demonstrate that cloning quantum states is, in-fact, equivalent to cloning the trash-and-replace channel and therefore the former is a special case of the more general problem. By appealing to higher-order quantum operations (quantum processes) we construct a unified framework to deal with the most general cloning tasks and establish necessary conditions for a family of channels to exhibit super-replication -- a quadratic cloning rate with vanishing error. We find that noisy phase-gate channels satisfy these conditions, and we construct the explicit super-replicating process for the task. Conversely, we find that the criteria are not met by the full set of noisy unitary gates; classical noise channels; or amplitude damping channels, whose respective cloning rates are at most linear. In this paradigm, we not only derive new results, but also refigure known ones. We derive a strong converse for state cloning, and for unitary channels we construct an alternative super-replication process to that of Dür et al. [PRL 114, 120503 (2015)] and Chiribella et al. [PRL 114, 120504 (2015)] based on a measure-and-prepare process, which allows us to establish a direct connection between optimal channel cloning and Bayesian channel estimation. Finally we give an SDP algorithm to search for optimal cloning processes and study the advantage of coherent vs measure-and-prepare protocols on concrete examples.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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