低秩量子信道的近最优非相干层析成像
Near-optimal incoherent tomography of low-rank quantum channels
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中文总结 AI 辅助
本研究针对低秩量子信道，提出近最优的非相干层析成像算法，在特定条件下达到最优查询复杂度，对一般信道则通过矩阵乘法权重更新实现近匹配上界。
中文摘要 AI 辅助
我们研究输入维度为 $d_1$、输出维度为 $d_2$、Kraus 秩至多为 $r$ 的量子信道的层析成像，在信道查询之间不保留量子存储的自适应实验中，达到金刚石范数误差 $\varepsilon$。对于非零 Choi 特征值下界为 $\Omega(d_1/r)$ 的量子信道，我们建立了最优查询上下界 $\Theta(d_1d_2r^2/\epsilon^2)$。上界由非自适应算法实现，该算法使用 [Surawy-Stepney 等人，Quantum (2022)] 中的估计器，并结合新的金刚石范数分析。下界适用于任意自适应非相干协议，并源于一个新的局部信道族和统一的单次查询 Fisher 信息界。对于一般信道，我们建立了上界 $O(d_1d_2r^2\log(2d_1)/\epsilon^2)$，几乎匹配上述下界 $\Omega(d_1d_2r^2/\varepsilon^2)$。为实现这一点，我们通过矩阵乘法权重更新算法，在 $O(\log(2d_1))$ 轮中调整输入状态，从而推广了上述非自适应算法。
英文摘要
We study tomography for quantum channels with input dimension $d_1$, output dimension $d_2$, and Kraus rank at most $r$, to within diamond norm error $\varepsilon$, using adaptive experiments that retain no quantum memory between channel queries. - For quantum channels whose non-zero Choi eigenvalues are bounded below by $Ω(d_1/r)$, we establish optimal query upper and lower bounds $Θ(d_1d_2r^2/ε^2)$. The upper bound is achieved by a nonadaptive algorithm that uses the estimator from [Surawy-Stepney et al., Quantum (2022)], together with a new diamond-norm analysis. The lower bound applies to arbitrary adaptive incoherent protocols and follows from a new local family of channels and a uniform one-query Fisher-information bound. - For general channels, we establish an upper bound $O(d_1d_2r^2\log(2d_1)/ε^2)$, nearly matching the above lower bound $Ω(d_1d_2r^2/\varepsilon^2)$. To achieve this, we generalize the above nonadaptive algorithm by adapting the input state over $O(\log(2d_1))$ rounds with the Matrix Multiplicative Weight Update algorithm.
发表机构
- University of Pennsylvania（宾夕法尼亚大学）
- University Mohammed VI Polytechnic（穆罕默德六世polytechnic大学）
机构由 AI 辅助整理，请以论文原文为准。
