论文标题
量子分布之间的kullback-leibler差异及其上限
Kullback-Leibler divergence between quantum distributions, and its upper-bound
论文作者
论文摘要
这项工作提出了一个高价值的值，即Kullback-Leibler（KL）差异可以达到一类称为量子分布（QD）的概率分布。目的是找到一个分配$ u $，该$ u $最大化kl差异与给定分布$ p $的假设是，$ p $和$ u $是通过分配给定的离散数量（量子）而产生的。量子分布自然代表了在实际应用中使用的广泛概率分布。此外，可以作为任何概率分布的近似值获得这样的分布。在此，在比较的分布是相同量子值的量子分布的条件下，在这里证明了熵差异的上限检索可能是可能的。因此，当熵差异将其应用于可比较的分布时，它会获得更强大的含义。在差异的未来发展中，应考虑这一方面。理论发现用于提出归一化KL差异的概念，该概念在经验上证明与已知的措施的行为不同。
This work presents an upper-bound to value that the Kullback-Leibler (KL) divergence can reach for a class of probability distributions called quantum distributions (QD). The aim is to find a distribution $U$ which maximizes the KL divergence from a given distribution $P$ under the assumption that $P$ and $U$ have been generated by distributing a given discrete quantity, a quantum. Quantum distributions naturally represent a wide range of probability distributions that are used in practical applications. Moreover, such a class of distributions can be obtained as an approximation of any probability distribution. The retrieving of an upper-bound for the entropic divergence is here shown to be possible under the condition that the compared distributions are quantum distributions over the same quantum value, thus they become comparable. Thus, entropic divergence acquires a more powerful meaning when it is applied to comparable distributions. This aspect should be taken into account in future developments of divergences. The theoretical findings are used for proposing a notion of normalized KL divergence that is empirically shown to behave differently from already known measures.
