发表机构
MIT（麻省理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究证明态层析在每次测量至多使用k个新拷贝且无量子内存时的拷贝复杂度下界，与已知上界匹配，消除了先前对k的限制，核心是仅依赖最小特征值的均匀Fisher信息界。
AI 中文摘要
我们研究当每次测量作用于至多 $k$ 个新拷贝且块之间不保留量子内存时的态层析问题。我们证明了一个与 [ arXiv:2510.07788 ] 中上界匹配的下界。因此，估计任意 $d$ 维态至迹距离 $\epsilon$ 的拷贝复杂度，在绝对常数因子内，对于每个 $k$ 和所有足够小的 $\epsilon$，为 $\max\{d^3/(\sqrt{k}\epsilon^2),d^2/\epsilon^2\}$。这消除了先前要求 $k$ 作为精度函数必须很小的限制。该下界适用于每个块内的任意测量以及块之间的自适应选择。该下界已经适用于任何最小特征值数量级为 $1/d$ 的态的小邻域内，即使中心已知。主要成分是一个均匀的 Fisher 信息界，用于一个测量块，该界仅依赖于态的最小特征值。证明避免了导致 [ arXiv:2402.16353 ] 中限制的微扰展开。Fano 不等式用于度量球，以及互信息和 Fisher 信息之间的对数 Sobolev 比较，然后将自适应协议归结为该块界 [ arXiv:1607.00550, arXiv:1902.08582 ]。
英文摘要
We study state tomography when each measurement acts on at most $k$ fresh copies and no quantum memory is retained between blocks. We prove a lower bound matching the upper bound in [arXiv:2510.07788]. Thus the copy complexity of estimating an arbitrary $d$-dimensional state to trace distance $ε$ is, up to absolute constant factors, $\max\{d^3/(\sqrt{k}ε^2),d^2/ε^2\}$ for every $k$ and all sufficiently small $ε$. This removes the earlier restriction that $k$ be small as a function of the accuracy. The lower bound applies to arbitrary measurements within each block and adaptive choices between blocks. The lower bound already applies in a small neighborhood of any state whose smallest eigenvalue is of order $1/d$, even when the center is known. The main ingredient is a uniform Fisher information bound for one measurement block that depends only on the smallest eigenvalue of the state. The proof avoids the perturbative expansion responsible for the restriction in [arXiv:2402.16353]. Fano's inequality for metric balls and a log-Sobolev comparison between mutual and Fisher information then reduce the adaptive protocol to this block bound [arXiv:1607.00550, arXiv:1902.08582].
Comments36 pages
