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 for PPT channels and 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的强化。因此，在需要对信息处理进行更深入分析的诸多场景中，它们具有许多自然的应用。然而，计算这些系数通常颇具挑战。作为解决方案，我们讨论了多布林系数的量子推广。这些系数为许多收缩系数提供了一个高效可计算的上界。我们证明了其若干性质，并讨论了推广与应用。特别地，我们给出了PPT信道更强有力的上界，并引入了限制某些膨胀系数的反向多布林系数。