针对 $p$ 接近 0 时最小输出 $p$-Renyi 熵可加性的反例
量子物理
2009-11-13 v3
摘要
作为对量子信息论中可加性猜想近期进展的补充（该进展表明信道的最小输出 -Renyi 熵在 时通常不可加），我们通过仔细的概率选择论证证明，在 时以及因此在足够小的 值下也存在反例。给出了一个从 4 维到 3 维的两个信道的显式构造，它们具有非乘性的最小输出秩；对于这对信道，数值计算强烈表明 -Renyi 熵在所有 时均不可加。然而我们猜想，对于所有 都存在可加性破坏。
引用
@article{arxiv.0712.3628,
title = {Counterexamples to additivity of minimum output p-Renyi entropy for p close to 0},
author = {Toby Cubitt and Aram W. Harrow and Debbie Leung and Ashley Montanaro and Andreas Winter},
journal= {arXiv preprint arXiv:0712.3628},
year = {2009}
}
备注
7 pages, revtex4; v2 added correct ref. [15]; v3 has more information on the numerical violation as well as 1 figure (2 graphs) - note that the explicit example was changed and the more conservative estimate of the bound up to which violations occur, additionally some other small issues are straightened out