AI 中文总结
该研究构造最小qutrit信道反例，推翻Lesniewski与Ruskai关于单随机映射下单调黎曼度量收缩系数的猜想，明确三维是反例存在的最小全矩阵代数维度。
AI 中文摘要
Lesniewski和Ruskai猜想：在单随机映射下，所有单调黎曼度量的收缩系数等于无迹子空间上的希尔伯特-施密特收缩。我们利用由双随机3×3矩阵诱导的可分性破缺qutrit信道，推翻该猜想。对于每个归一化单调度量，忠实对角态与可交换无迹切向量同时给出精确下界：η^Riem_κ(Φ_K)≥8896/20007>(62+2√61)/225=Λ₂(Φ_K^†Φ_K)。该反例在极大阿贝尔子代数上完全经典。Hiai和Ruskai的定理确立了该猜想对所有单量子比特映射成立，因此在全矩阵代数中，三维是最小的。
英文摘要
Lesniewski and Ruskai conjectured that the contraction coefficient of every monotone Riemannian metric under a unital stochastic map equals the Hilbert--Schmidt contraction on the traceless subspace. We disprove the conjecture with an explicit entanglement-breaking qutrit channel induced by a doubly stochastic $3\times3$ matrix. A faithful diagonal state and a commuting traceless tangent give, simultaneously for every normalized monotone metric, the exact lower bound $η^{\mathrm{Riem}}_κ(Φ_K)\ge 8896/20007>(62+2\sqrt{61})/225=Λ_2(Φ_K^{\dagger}Φ_K)$. The counterexample is entirely classical on a maximal abelian subalgebra. A theorem of Hiai and Ruskai establishes the conjectured identity for all unital qubit maps, so dimension three is minimal among full matrix algebras.
Comments6 pages. Exact qutrit counterexample; AI-use disclosure included
