发表机构
The University of Hong Kong（香港大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对并行查询下酉信道层析成像的效率问题，提出新协议以O(d²/ε)次并行查询达到金刚石距离ε精度，匹配下界，弥合并行与顺序策略差距，并优化了边界区域及费米子线性光学层析成像的查询复杂度。
AI 中文摘要
在量子过程层析成像的研究中，如何以严格并行的查询方式，像顺序查询那样高效地学习一个酉信道在金刚石距离下的性质，一直是一个悬而未决的问题。顺序查询允许利用自适应性来细化估计并相应调整学习策略，而并行查询则无法进行此类调整。从高阶量子操作的角度来看，任何并行学习策略都可以由顺序策略模拟，而反之则通常不成立，这表明顺序学习策略可能更强大。与这一直觉相反，我们提出了一种新协议，使用$\mathcal{O}(d^2/\varepsilon)$次并行查询，在金刚石距离内学习一个未知的$d$维酉信道至$\varepsilon$精度，匹配了[Haah, Kothari, O'Donnell, and Tang, FOCS '23]中给出的下界。我们的协议因此弥合了酉信道层析成像中并行与顺序策略之间的差距。作为应用，该协议在边界区域量子信道层析成像中实现了最优查询复杂度，并提高了费米子线性光学层析成像中已知最佳协议的查询效率。
英文摘要
In the study of quantum process tomography, it has remained open how to learn a unitary channel in diamond distance with strictly parallel queries as efficiently as with sequential queries. Sequential queries allow one to exploit adaptivity to refine the estimate and adjust the learning strategy accordingly, whereas such adjustments are impossible for parallel queries. From the perspective of higher-order quantum operations, any parallel learning strategy can be simulated by a sequential one, whereas the converse does not hold in general, suggesting that sequential learning strategies are potentially more powerful. Contrary to this intuition, we present a new protocol for learning an unknown $d$-dimensional unitary channel to within $\varepsilon$ in diamond distance using $\mathcal{O}(d^2/\varepsilon)$ parallel queries, matching the lower bound presented in [Haah, Kothari, O'Donnell, and Tang, FOCS '23]. Our protocol thus closes the gap between parallel and sequential strategies for unitary channel tomography. As applications, it achieves optimal query complexity for boundary-regime quantum channel tomography and improves the query efficiency of the best-known protocol for tomography of fermionic linear optics.
Comments30 pages. Comments are welcome
