发表机构
Universidade Federal Rural de Pernambuco（伯南布哥联邦农村大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究测量量子散度的非凸优化，证明在光滑生成元下投影局部最优即全局最优，并给出分块判据，应用于二进制可访问信息与Rényi散度，解决相关猜想。
AI 中文摘要
我们研究了秩一投影测量上测量量子$f$-散度的非凸优化。对于光滑的算子-Fenchel可提升生成元和忠实态，每个投影局部最大值和每个二阶驻点在所有POVM上都是全局最优的。该判据是分块的：一个临界PVM是最优的当且仅当压缩态在每个等分块上成比例；否则，一个显式的两向量旋转具有正上升曲率。算子凸生成元允许正原子曲率分解，二次$\chi^2$情形产生双侧残差界。对于二进制可访问信息，该框架证明了已知的自适应容量等式，并表明每个非相同量子比特系综恰好有两个驻点投影测量，证明了Keil和Thai--Dall'Arno的猜想。一个稀有先验极限将加权Jensen-Shannon信息与相对熵联系起来，并产生一个有限反例，以反驳观测熵与全系综互信息阶之间提出的等价性。景观定理还涵盖了有限正阶的测量Rényi散度和测量相对熵。
英文摘要
We study nonconvex optimization of measured quantum $f$-divergences over rank-one projective measurements. For smoothly operator-Fenchel liftable generators and faithful states, every projective local maximum and every second-order stationary point is globally optimal over all POVMs. The criterion is blockwise: a critical PVM is optimal exactly when the compressed states are proportional on each equal-score block; otherwise an explicit two-vector rotation has positive ascent curvature. Operator-convex generators admit a positive atomic curvature resolution, and the quadratic $χ^2$ case yields two-sided residual bounds. For binary accessible information, this framework proves the known adaptive-capacity equality and shows that every nonidentical qubit ensemble has exactly two stationary projective measurements, proving conjectures of Keil and Thai--Dall'Arno. A rare-prior limit connects weighted Jensen--Shannon information to relative entropy and yields a finite counterexample to the proposed equivalence between observational-entropy and all-ensemble mutual-information orders. The landscape theorem also covers measured Rényi divergences of finite positive order and measured relative entropy.
Comments42 pages, 2 figures. Source and reproducible assets: https://github.com/DomingosSalazar/benign-projective-landscapes
