Year: 2026
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Ru, Shihao, Li, Bikun, Gao, Weibo, Jiang, Liang
Institutions: Nanyang Technological University, University of Chicago
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funders: National Science Foundation, U.S. Department of Energy, National Research Foundation Singapore, Ministry of Education, India, Defense Advanced Research Projects Agency, Office of Science, Multidisciplinary University Research Initiative, Office of Naval Research, Advanced Scientific Computing Research, Air Force Office of Scientific Research, Army Research Office
Awards: G102163711, G1404049065, QuSeC-TAQS: Nanoscale Covariance Magnetometry with Diamond Quantum Sensors, G1515916119, G1657001476, G1932254719, G2095623760, G2145085266, G2282031079, G2287611682, G2443537725, G262962599, G2882288540, G3162985271, G3316082199, G431725244, G4848018484, G498139845, G513797252, G5398989114, G6518383159, G6547089213, G6918803902, G741291543, G8343797021, ExpandQISE: Track 2: Developing Quantum Information Science and Engineering Research and Education Program at FAMU, G878601127, G96630211, G993149817
OpenAlex ID: W7215094145