论文标题
连贯性作为Tsallis和Renyi熵的熵增量
Coherence as entropy increment for Tsallis and Renyi entropies
论文作者
论文摘要
相干性的相对熵可以写为原始状态的熵差，并且在通过相对熵测量时最接近它的不一致状态。自然的问题是，如果我们将这种情况推广到Tsallis或Rényi熵，它是否会定义良好的连贯措施？换句话说，我们定义了原始状态的tsallis熵与最接近它的不一致状态之间的差异。以Rényi熵而不是Tsallis熵，导致了众所周知的基于距离的Rényi连贯性，这意味着该表达式定义了一个良好的连贯性度量。有趣的是，我们表明Tsallis熵甚至不会产生真正的连贯性单调，除非它处于非常限制的操作类别之下。此外，我们还提供了Tsallis和Rényi相干表达式的连续性估计。此外，当tsallis或rényi相对熵测量时，我们基于最接近的不一致状态提出了两种连贯措施。
Relative entropy of coherence can be written as an entropy difference of the original state and the incoherent state closest to it when measured by relative entropy. The natural question is, if we generalize this situation to Tsallis or Rényi entropies, would it define good coherence measures? In other words, we define a difference between Tsallis entropies of the original state and the incoherent state closest to it when measured by Tsallis relative entropy. Taking Rényi entropy instead of the Tsallis entropy, leads to the well-known distance-based Rényi coherence, which means this expression defined a good coherence measure. Interestingly, we show that Tsallis entropy does not generate even a genuine coherence monotone, unless it is under a very restrictive class of operations. Additionally, we provide continuity estimates for both Tsallis and Rényi coherence expressions. Furthermore, we present two coherence measures based on the closest incoherent state when measures by Tsallis or Rényi relative entropy.
