There was a startup company I met with a long time ago that was selling QKD to Wall St. They kept saying that sales were the proof that it worked. I’m not so sure they were actually doing it right.

For some background, the security of QKD relies on a very ‘lucky’ chain of events. I will try to detail it from (very old) memory. Please, I encourage you to look it up and correct me.

First you need to generate a single coherent photon. This is impossible with a LED, so you have to pump it to threshold and then use a neutral-density filter to get one photon out. You cannot control this because both generation and absorption in the filter are random processes following Poisson statistics. So no matter what you do, you get a random stream of photons separated by exponential time distribution, and you want to set that time constant such that you are very unlikely to get more than one photon per time slice, because this can cause a measurement mismatch and ruin the whole key.

Then you have a 50% silvered mirror to split the photon state where it can either pass through a polarizer or not, and then combine these two states back into the same beam. Lossless combining is not trivial. Most setups just use another half-silvered mirror, but that cuts the probability of achieving coherent superposition by 75%.

Then you have to double that coherent state using maybe erbium-doped fiber. Exactly once, no losses. This is also a statistical phenomenon, and I forget the distribution of the number of doublings, but the protocol requires some high probability of exactly one. Note that at this point, you can start cheating by pumping the power and the key will still get transferred without mismatch errors, because you are amplifying a superposition state. The security, however, still depends on single photons.

Now split again, same half-silver mirror trick. You need a perfect split of one photon each way, which has a 50% probability. One of these photons gets measured by the sender, and the other gets sent to be measured by the receiver. The one that goes to the receiver has to make it through an un-amplified fiber without any losses. This is also a statistical phenomenon and of course very unlikely at significant distance.

Now we are at the measurement phase. We take a random choice of mirror orientation to measure either the transverse or circular polarization state. Split again by half and pass the amplified state through a Polaroid disk of each orientation and then collect at a photomultiplier tube. There is only a 50% chance of the photon going down the right path to be detected, but if you do get a signal, then you have a fairly good probability that you are making the correct call.

Then, you tell the other side which type of polarization you measured at each side, and whether you got any signal, but not which signal, and the key is the result from each state which was measured in the same way and both sides got a signal. So there is another 50% probability of matching.

I’ll not do the math, but you can see how unlikely this is, even in perfect conditions. Buts it’s easy to cheat in several ways to get a key that is consistent among participants, but not actually secure to eavesdroppers. I suppose you’d want to layer this along with Diffe-Hellman anyway though, so I guess it can’t hurt.