AI 中文总结
该研究完成了α>2时极大Rényi相对熵的特征刻画，确定其形式为z=α-1的α-z Rényi相对熵，并应用该结果明确了吉布斯保操作在催化场景下的相干生成能力。
AI 中文摘要
量子相对熵在量子信息理论中具有基础作用。在经典场景下，Rényi相对熵经线性组合后构成最通用的相对熵类，自然推动了对其最小与最大量子扩展形式的探索。已知最小扩展在α∈[0,1/2)时为反向夹积Rényi相对熵，在α≥1/2时为夹积Rényi相对熵。相比之下，此前仅在α∈[0,2]时确定了最大扩展，其形式为几何Rényi相对熵。本研究完成了这一特征刻画，证明当α>2时，最大扩展的形式为z=α-1的α-z Rényi相对熵。作为应用，研究确定了在无关联催化剂辅助下，能量非相干态可通过吉布斯保操作转化为能量相干态的条件，从而完整刻画了该类操作在催化场景下的相干生成能力。
英文摘要
Quantum relative entropies play a fundamental role in quantum information theory. In the classical setting, Rényi relative entropies constitute, up to linear combinations, the most general class of relative entropies, naturally motivating the search for their minimal and maximal quantum extensions. The minimal extension is known to be the reverse sandwiched Rényi relative entropy for $α\in[0,1/2)$ and the sandwiched Rényi relative entropy for $α\geq 1/2$. In contrast, the maximal extension had previously been identified only for $α\in[0,2]$, where it is given by the geometric Rényi relative entropy. In this work, we complete this characterization by proving that for $α>2$, the maximal extension is given by the $α$-$z$ Rényi relative entropy with $z=α-1$. As an application, we determine when an energy-incoherent state can be transformed into an energy-coherent state by a Gibbs-preserving operation assisted by an uncorrelated catalyst, thereby fully characterizing the coherence-generating power of this class of operations in the catalytic setting.
