Abstract

We consider the problem of decoupling a given bipartite state under various constraints which make the decoupling task highly non-trivial. Among these, stand as notable examples the Landauer-like approach (where one minimises the amount of “work” necessary for decoupling) and the geometrical approach (where contraints are given as covariance properties of the decoupling map). Correspondingly, one obtains quantitative measures for the strength or amount of correlations present in the input state.

In this talk, I propose and study a model of decoupling where the constraint can be understood as a sort of security requirement: the amount of correlations that can be transferred into the environment during the decoupling process has to be upper-bounded by some security/leakage parameter. As a consequence, it turns out that, in general, total correlations can be only partially erased. Bounds for the one-shot case, as well as some results for the i.i.d. asymptotic limit are given.