I. Introduction
In quantum mechanics, every noisy channel (completely positive and trace preserving – CPTP – linear map) is the marginal of a reversible (i.e. unitary) interaction with an environment initially in a pure state; this is the content of Stinespring’s dilation theorem [30], and of the subsequent structure theorems of Choi [6], Jamiołkowski [15] and Kraus [18]. This feature, which distinguishes quantum communication fundamentally from its classical counterpart, is at the core of the possibility to perform unconditional secret key agreement over a channel, since the channel essentially uniquely determines the action on the environment. In this picture, noise in the channel is entirely due to loss of information into the environment, more precisely the build-up of correlations between the system and the environment. A series of prior work, starting with [9], [10] have asked how much one can counteract the noise if one had access to the environment output state and could feed classical information back into the channel output system [11], [20], [21], [29], [34].