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Peer-reviewedCC BY 4.0Quantum

A Counterexample to the Optimality Conjecture in Convex Quantum Channel Optimization

  • Jianting Yang1,2
  1. 1School of Mathematical Sciences, University of Electronic Science and Technology of China
  2. 2State Key Laboratory of Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences
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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.

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Cite

BibTeXRIS
BibTeX
@article{yang2026counterexample,
  title = {{A Counterexample to the Optimality Conjecture in Convex Quantum Channel Optimization}},
  author = {Jianting Yang},
  journal = {Quantum},
  year = {2026},
  month = oct,
  doi = {10.22331/q-2026-10-28-2253},
  url = {https://quantum-journal.org/papers/q-2026-10-28-2253/},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - A Counterexample to the Optimality Conjecture in Convex Quantum Channel Optimization
AU  - Jianting Yang
PY  - 2026
DA  - 2026/10/28
JO  - Quantum
DO  - 10.22331/q-2026-10-28-2253
UR  - https://quantum-journal.org/papers/q-2026-10-28-2253/
AB  - 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.
SN  - 2521-327X
ER  -