# What is the difference between CV QKD and DV QKD?

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).

• "uses infinite dimensional systems", I know my question might be bit dumb, but if is infinite dimension, does it mean without bounds? if so, then how can such QKD real-world device be created? or do we mean infinite here as in for example "continuous probability distribution" where we have infinite amount of points between any 2 points? Oct 31, 2021 at 18:14
• The dimension refers to dimension of the Hilbert space that describes the system. Many real world systems are described by infinite dimensional Hilbert spaces. Consider having a read of this answer to learn a bit more about them. I'm not sure what you mean by "without bounds" but yes in a sense you can think about some of these systems as being generalizations of continuous probability distributions like finite dimensional systems can be seen as generalizations of discrete probability distributions. Oct 31, 2021 at 18:25

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.