Quantum Cryptography is a phrase that seems to bleed across two topics - one is QBit Cryptanalysis, and the other is Quantum Key Exchange (which is the most common use of the term, and I will discuss here)
With Quantum Key Exchange, you use a single optical fiber to send a single photon at a time orientated to one certain angle of four; we can describe them as horizontally polarized ( - ), vertically polarized ( | ), Ordinary ( \ ) or Sinister ( / ) To detect these photons, you can use either an ordinary filter ( \ slot) or a vertical filter ( | slot)
An ordinary filter has the properties that it will always pass an ordinary polarized photon, and always block a sinister polarized photon (this is because the photon is correctly aligned for the slot in the Ordinary case, and at to the slot for the Sinister photon.
A vertical filter has similar properties for its two associated photons - it will always pass a vertical photon, and always block a horizontal one.
This leaves four cases: '|' and '-' for an ordinary filter, and '\' and '/' for a vertical one. The problem is - nobody knows! they might make it though the slot, they might not, and it is entirely random.
For this reason, the sender will send 'n' photons to the recipient, and the recipient will then report back which of the two possible filters (chosen at random) he tried.
If the recipient guessed the right filter, he now knows which one of two possible orientations the photon was in. if he guessed wrong, he has no idea - so the sender responds to the recipient's list with a second list - of the decisions the recipient got right. By discarding the "wrong" filter choices, both sender and recipient now know which of two possible choices each of the photons received were actually matched to - and can convert pass/fail into logic 1 or 0 for a binary set (and this can then be used as an encryption key)
However, this *only* works if the cable between the sender and the recipient is completely unbroken - because it is impossible to route, regenerate or otherwise manipulate the photons sent without losing the delicate orientation information that is the hub of the scheme.
Anybody who tries to measure the photons en route must pick the correct filter - if he picks the wrong one, he is unable to tell the difference between a pass and a misaligned photon that happens to have gotten though the slot - and indeed, a block and a misaligned photon that was blocked. If he picks wrongly, he cannot tell what orientation the photon was in, and the eventual conversation between the recipient and sender as to orientation of filters will cause there to be differences between the two sets of data - and reveal an eavesdropper has intercepted photons.
There are obvious problems with this scheme. the first is that sending a single photon down a light pipe can be unreliable - sometimes, they fail to reach the recipient and are read as a false "block". The second is that the obvious attack on this is a man-in-the-middle one - the attacker intercepts both the light pipe and the out-of-band data channel used for the discussion of filters and acceptance lists - then negotiates different Quantum key Exchange keysets with both the sender and the recipient independently. by converting the encrypted data between the keys each is expecting to see, he can read the message en route (provided of course there is no way that either party can verify the transmissions in a way the m-i-t-m cannot intercept and replace with his own doctored version)
However, the problems have not stopped a commercial company selling a product which relies on QKE for its operation.