aiqbench analysis
This is a narrow mathematical result in quantum information theory: a 2-dimensional counterexample showing that a proposed optimality condition for trace-distance state transformation does not hold in general. It matters mainly to researchers working on quantum channel optimization and resource theories, since the Coutts et al. dual-certificate conjecture was a candidate tool for characterizing optimal solutions. The work corrects a claim rather than introducing a new capability, so its impact is on theory, not on near-term quantum hardware or applications.
A Counterexample to the Optimality Conjecture in Convex Quantum Channel Optimization
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.
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.
Quantum Physics (quant-ph); Optimization and Control (math.OC)
arXiv:2512.22863 [quant-ph]
(or arXiv:2512.22863v3 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2512.22863 Focus to learn more arXiv-issued DOI via DataCite
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