Generalized Reimpell-Werner Iteration

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.

arXiv:2609.40203 [quant-ph]

(or arXiv:2609.40203v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.40203 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.