preparation noise (e.g., due to imperfections in the optical switches/modulators or coming from the natural thermal background at lower frequencies [Filip,Usenko,Weedbrook2010,Weedbrook2012,Weedbrook2014]{}) as well as measurement noise and inefficiencies affecting the detectors (which could be genuine or even added by the honest parties [@Renner2005; @Pirandola2009]). Such trusted noise may be high enough to prevent the distribution and distillation of entanglement, but still a secure key can be extracted due to the presence of non-zero discord.

By contrast, if the extra noise in the apparata is not trusted but considered to be the effect of side-channel attacks [@SideCH], then we have to enforce device-independent QKD [@Ekert]. In this more demanding scenario, quantum discord is still necessary for security but more simply becomes an upper bound to the coherent information. This means that secure key distribution becomes just a consequence of entanglement distillation.

*Quantum discord.*– Discord comes from different quantum extensions of the classical mutual information. The first is quantum mutual information, measuring the total correlations between two systems, $A$ and $%
B $, and defined as $I(A,B):=S(A)-S(A|B)$, where $S(A)$ is the entropy of system $A$, and $S(A|B):=S(AB)-S(B)$ its conditional entropy. The second extension is $C(A|B):=S(A)-S_{\min}(A|B)$, where $S_{\min}(A|B)$ is the entropy of system 