🤖 AI Summary
研究了两量子位经典状态下Rényi纠缠纯化在不同阶数下的可加性问题，通过精确求解单副本优化和限制双副本优化证明了α∈[0,1)时的非可加性。
📝 Abstract
Entanglement of purification is a fundamental measure of total correlations whose additivity remains unresolved. We study its additivity for classical states on two qubits at different Rényi orders. For every $α\in[0,1)$, we prove nonadditivity within this family, witnessed by two copies of a single state. We first solve the one-copy optimization exactly for the entire family at every Rényi order. We then restrict the two-copy optimization to a natural finite set of purifications and exhibit one whose entropy is strictly below the product value. In contrast, for $α\in[2,\infty]$ we prove additivity under tensor products within this family. The interval $α\in[1,2)$, including the von Neumann case $α=1$, remains open, and we conjecture additivity there throughout the same family.