广义Reimpell-Werner迭代
Generalized Reimpell-Werner Iteration
- Nanyang Technological University（南洋理工大学）
- University of Chicago（芝加哥大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
该研究将Reimpell-Werner迭代推广至任意厄米代价矩阵的线性目标，证明在支撑重叠条件下收敛至全局最优，并给出O(1/ε)迭代复杂度，为量子测量和信道优化提供了严格基础。
AI中文摘要：
量子测量和量子信道决定了信息在量子协议中如何被提取、编码和传输。优化它们的性能通常需要数值方法，这些方法在希尔伯特空间维度增加时仍需保持实用性。Reimpell-Werner迭代通过重复的矩阵更新并遵守约束条件，为这些任务提供了一种实用的方法。在此，我们将该迭代推广到具有任意厄米代价矩阵的线性目标函数。我们证明了当初始化满足适当的支撑重叠条件时，迭代收敛到全局最优。对于每个固定问题、迭代参数的选择和可允许的初始化，渐近地，O(1/ε)次迭代足以使目标值达到最优值的ε范围内。这些结果为该迭代提供了严格的基础，并拓宽了其收敛保证适用的优化问题类别。
英文摘要：
Quantum measurements and channels determine how information is extracted, encoded, and transmitted in quantum protocols. Optimizing their performance often requires numerical methods that remain practical as Hilbert space dimensions increase. The Reimpell-Werner iteration offers a practical approach to these tasks through repeated matrix updates that respect the constraints. Here, we generalize this iteration to linear objectives with arbitrary Hermitian cost matrices. We prove that the iterates converge to a global optimum whenever the initialization satisfies suitable support overlap conditions. For each fixed problem, choice of iteration parameters, and admissible initialization, $\mathcal{O}(1/\varepsilon)$ iterations suffice asymptotically to bring the objective value within $\varepsilon$ of the optimum. These results provide a rigorous foundation for the iteration and broaden the class of optimization problems to which its convergence guarantees apply.
