关于无逆查询的状态区分

中文摘要 AI 辅助

在量子态区分问题中，算法被给予一个量子态 $|\psi\rangle$ 或 $|\phi\rangle$ 的若干副本，两态之间的迹距离为 $\varepsilon$，任务是判断实际是哪个态。标准结果是需要 $\Theta(\varepsilon^{-2})$ 个副本，而如果能够访问酉态制备预言机及其逆，则查询次数可改进为 $\Theta(\varepsilon^{-1})$。我们研究仅前向访问的中间情形，这对应于预言机是不可逆物理过程的场景。Tang 和 Wright 最近证明，在高维空间中，区分一个已知态与一个未知的邻近态需要 $\Omega(\varepsilon^{-2})$ 次前向查询；我们加强了这一结果，证明即使两个态都是已知的（如在状态区分设置中），同样的下界仍然成立。此外，我们的下界使用直接混合论证，避免了先前工作中使用的高级压缩预言机技术。相比之下，我们给出一个与维度无关的算法，解决状态区分的连续时间变体，仅需 $O(\varepsilon^{-1})$ 的总前向演化时间。该算法利用量子 Zeno 动力学将演化限制在一个已知的二维子空间内。因此，对于状态区分的自然连续时间类比，二次优势在没有逆访问的情况下仍然存在。

英文摘要

In the quantum state distinguishing problem, an algorithm is given copies of a state $|ψ\rangle$ or $|ϕ\rangle$ separated by trace distance $\varepsilon$, and tasked with deciding which is the case. It is a standard result that $Θ(\varepsilon^{-2})$ copies are required, while having access to a unitary state preparation oracle and its inverse improves this to $Θ(\varepsilon^{-1})$ queries. We study the intermediate case with forward-only access, capturing scenarios where the oracle is a physical process that cannot be reversed. Tang and Wright recently showed that distinguishing a known state from an \emph{unknown} close state requires $Ω(\varepsilon^{-2})$ forward queries in high dimension; we strengthen this result by proving the same bound even when both states are known, as in the state distinguishing setting. Moreover, our lower bound uses a direct hybrid argument, avoiding advanced compressed oracle techniques used in the prior work. In contrast, we give a dimension-independent algorithm solving a continuous-time variant of state distinguishing with only $O(\varepsilon^{-1})$ total forward evolution time. The algorithm uses quantum Zeno dynamics to confine evolution to a known two-dimensional subspace. Thus, a quadratic advantage survives without inverse access for a natural continuous-time analogue of state distinguishing.

发表机构

• White Station High School（白站高中）
• University of Maryland（马里兰大学）

机构由 AI 辅助整理，请以论文原文为准。