Quasi chain rule for min-entropy

The classical Shannon's entropy possesses a natural definition of conditional entropy and a useful chain rule whose application is ubiquitous in information theory. On the contrary, for the case of min-entropy both: the definition of conditional min-entropy and the formulation of chain rule are still subject of discussion. This paper goes along this line of research and proposes new candidate for chain rule for conditional min-entropy as defined in Dodis et al. paper [1]. We derive our quasi chain rule based on so-called spoiling knowledge idea.