A Counterexample to the Optimality Conjecture in Convex Quantum Channel Optimization

Jianting Yang

doi:10.22331/q-2026-10-28-2253

A Counterexample to the Optimality Conjecture in Convex Quantum Channel Optimization

School of Mathematical Sciences, University of Electronic Science and Technology of China
State Key Laboratory of Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences

Published:	2026-10-28, volume 10, page 2253
Editor:	Jordi Tura
Eprint:	arXiv:2512.22863v3
Doi:	https://doi.org/10.22331/q-2026-10-28-2253
Citation:	Quantum 10, 2253 (2026).

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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.

► BibTeX data

@article{Yang2026counterexampleto,
  doi = {10.22331/q-2026-10-28-2253},
  url = {https://doi.org/10.22331/q-2026-10-28-2253},
  title = {A {C}ounterexample to the {O}ptimality {C}onjecture in {C}onvex {Q}uantum {C}hannel {O}ptimization},
  author = {Yang, Jianting},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {10},
  pages = {2253},
  month = oct,
  year = {2026}
}

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