I know what QKD is, as a concept but I recently found papers mentioning continuous-variable quantum key distribution , and discrete-variable quantum key distribution . So I would like to know what is the difference between them?
Also, when we generally say "QKD" only (without specifying), does it usually refer to DV-QKD?
Thanks
It's the dimension of the Hilbert spaces. In DV-QKD you have a finite dimensional Hilbert space (like a qubit). Thus your measurement outcomes come from a finite set. On the other hand a CV-QKD protocol uses infinite dimensional systems and therefore you can have a continuum of measurement outcomes.
If there's no specification as to whether a QKD scheme is CV or DV then I would guess that it's DV (but it should be relatively straightforward to work out from the mathematics as the CV schemes often require a slightly more careful treatment).
One example to understand it, if someone finds it useful, is the following:
Most QKD is done by sending light through a channel. In DV-QKD we send single photons through the channel, one at a time. We encode the information, for instance, in the polarization of each photon. In CV-QKD we send a continuous beam of light, as in most classical optical communications. The information can be encoded, for instance, by modulating the amplitude and phase of the electromagnetic wave.
The first QKD protocols were DV, as the BB84 protocol (1984). CV-QKD protocols were proposed in the 2000s. So the article's year of publication may give you a clue. I would say that if someone is just introducing the concept of QKD (as in an undergraduate course) he would be referring to DV-QKD rather than CV-QKD.
