任意维度下噪声幺正信道的渐近最优纯化
Asymptotically optimal purification of noisy unitary channels in any dimension
AI总结：
该研究解决任意维度下噪声幺正信道的渐近最优纯化问题，推导最优保真度，给出SU(d)协变并行策略，明确查询复杂度并分析其扩展性，还证明噪声幺正共轭对偶任务的最优保真度与纯化任务的主导阶结果一致。
AI中文摘要：
我们研究噪声幺正纯化问题：给定未知d维幺正信道及强度为p的去极化噪声，目标是构造一个超信道，将该噪声幺正通用纯化回原始未知幺正。我们对任意自适应序贯策略进行优化，解析推导噪声强度和信道使用次数主导阶下的最优保真度，同时提供一个具体的SU(d)协变并行策略，该策略可达到最优值。我们的结果表明，在低噪声 regime 中，实现主导阶失真度ε的查询复杂度为Θ(d²p/ε)，其扩展性优于结合最优态纯化与量子信道存储-检索的朴素方法。我们还研究噪声幺正共轭的对偶问题，目标是从噪声查询中获取原始未知幺正复共轭的最佳近似，证明该任务的最优保真度在低噪声和大查询极限下与噪声幺正纯化的主导阶最优保真度一致。
英文摘要：
We consider the problem of noisy unitary purification. Given access to an unknown $d$-dimensional unitary channel followed by depolarizing noise of strength $p$, we aim to construct a superchannel that universally purifies the noisy unitary back to the original unknown unitary. We optimize over arbitrary adaptive sequential strategies and analytically derive the optimal fidelity to the leading order in the noise strength and number of channel uses, while also providing a concrete $\mathrm{SU}(d)$-covariant parallel strategy that attains the optimum. Our result implies the query complexity $Θ(d^2p/ε)$ for achieving leading-order infidelity $ε$ in the low-noise regime, which scales better than the naive approach combining optimal state purification and storage-and-retrieval of quantum channels. We also consider the dual problem of noisy unitary conjugation, where the goal is to obtain the best approximation of the complex conjugate of the original unknown unitary from access to noisy queries. We show that the optimal fidelity for this task coincides with that of noisy unitary purification to the leading-order in the low-noise and large-query limit.
