state preparation and perfect detections).

This is an ideal scenario where system $P$ of Fig. \[PicD\] is simply absent. For such ideal QKD protocols, the secret-key rates satisfy again Eqs. (\[standard\]), (\[B1\]), and (\[B2\]), computed on the corresponding output states. Remarkably, the discord bound can be found to be tight in reverse reconciliation. In fact, as we show in the supplementary material, we can have $K(\blacktriangleleft)=D(B|A)$ in an ideal protocol of continuous-variable QKD, where Alice transmits part of an Einstein-Podolsky-Rosen (EPR) state over a pure-loss channel, such as an optical fiber.

*Conclusion and discussion*.– Quantum discord can be regarded as a bipartite formulation of non-orthogonality, therefore capturing the minimal requisite for QKD. In this paper we have identified the general framework, device-dependent QKD, where discord remains the ultimate cryptographic primitive able to guarantee security in the place of quantum entanglement.

We have considered a general form of device-dependent protocol, where Alice and Bob share a bipartite state which can be purified by two systems: One system ($E$) is accessible to Eve, while the other ($P$) is inaccessible and accounts from the presence of trusted noise, e.g., coming from imperfections in the state preparation and/or the quantum detections. This is a 