Contraction coefficients give a quantitative strengthening of the data processing inequality. As such, they have many natural applications whenever closer analysis of information processing is required. However, it is often challenging to calculate these coefficients. As a remedy we discuss a quantum generalization of Doeblin coefficients. These give an efficiently computable upper bound on many contraction coefficients. We prove several properties and discuss generalizations and applications. In particular, we give additional stronger bounds. One especially for PPT channels and one for general channels based on a constraint relaxation. Additionally, we introduce reverse Doeblin coefficients that bound certain expansion coefficients.

翻译：收缩系数为数据处理不等式提供了定量强化。因此，在需要对信息处理进行更精细分析时，它们具有许多天然的应用。然而，计算这些系数通常具有挑战性。作为补救，我们讨论了Doeblin系数的量子推广。这些系数为许多收缩系数提供了一个可高效计算的上界。我们证明了若干性质，并讨论了推广与应用。特别地，我们给出了额外的更强上界：一个专门针对PPT信道，另一个则基于约束松弛适用于一般信道。此外，我们引入了反向Doeblin系数，用以界定某些扩张系数。