device-dependent QKD, we can indeed build protocols which are secure ($K>0$) despite entanglement being completely absent (in any form, distillable or bound). Clearly, this is possible as long as the minimal condition $D(A|a)>0$ is satisfied. A secure protocol based on separable Gaussian states is explictly shown in the supplementary material.

In general, there is an easy way to design device-dependent protocols which are secure and free of entanglement. Any prepare and measure protocol whose security is based on the transmission of non-orthogonal states $\{\rho
_{a}(x),p_{x}\}$ can be recast into a device-dependent protocol, which is based on a classical-quantum state $\rho_{Aa}$ as in Eq. (\[cqSTATE\]), whose classical part $A$ is detected while the quantum part $a$ is sent through the channel. This is as secure as the original one as long as the purification of the classical-quantum state is inaccessible to Eve. Thus in such assumption of trusted noise, any prepare and measure protocol has an equivalent discord-based representation, where non-zero discord guarantees security in the place of non-orthogonality.

*Side-channels and device-independent QKD*.– Let us consider the more demanding scenario where all sources of noise are untrusted. This means that the extra noise in Alice’s and Bob’s apparata comes from side-channel 