A Counterexample to the Optimality Conjecture in Convex Quantum Channel Optimization

2026-10-26 · arXiv Quantum Physics

arXiv:2512.22863v3 Announce Type: replace

Abstract: This paper presents a counterexample to the optimality conjecture for the trace distance based optimal state transformation problem proposed by Coutts et al. [Quantum 5, 448 (2021)]. The conjecture posits that for the trace distance based optimal state transformation problem, applying the sign function to the error matrix uniquely determines a dual certificate for every optimal solution. By constructing a counterexample in 2-dimensional Hilbert spaces, we disprove this conjecture.

原文链接：https://arxiv.org/abs/2512.22863

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