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Generate two entangled photons, send one to a message sender and the other to the intended receiver. Both the sender and the receiver recover the same piece of quantum information from the photons, then the sender scrambles the message to be sent by some reversible function determined by the quantum information, and send this scrambled data to the receiver who is now capable of unscrambling it thanks to having the quantum information that was used for the scrambling procedure.

This description as far as I can tell would be a valid simplified explanation of both quantum cryptography and quantum teleportation. What exactly is the difference between the two terms?

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@Qmechanic What makes you think that this question has anything to do with teleportation? –  eBusiness May 14 '12 at 21:27
I guess we don't have an actual quantum-teleportation tag. Maybe we should? –  David Z May 14 '12 at 21:34

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The main difference between quantum cryptography and quantum teleportation is the following :

  • quantum teleportation aims at transmitting quantum information (i.e. a quantum state). Because of the no-cloning theorem, if the quality of this transmission is high enough, no-one except the legitimate receiver can reconstruct the quantum state, nor get any information about it.
  • quantum cryptography aims$^*$ at transmitting classical information privately. One way to do it is to encode the information on a quantum state, and then send this state through teleportation. This method is not very practical theoretically, but as far as I know, the best security proofs we have on the security of quantum cryptography protocols can be decomposed as :
    1. This (technologically doable) set-up can be shown to be equivalent to a (much more difficult to build but easier to analyse) teleportation based set-up;
    2. The equivalent teleportation set-up works well enough to guarantee the privacy of the communication.

So the analogy between quantum teleportation and quantum cryptography is very deep, and not a mere coincidence.

$*$ I know that some quantum cryptography protocols have other aims than privacy. But I don't think it's the subject of this question.

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Ok, that goes a bit of the way towards explaining it. But if a quantum cryptography setup doesn't use a real quantum teleportation channel, then what exactly is the difference between what the quantum cryptography hardware and the quantum teleportation hardware does? –  eBusiness May 22 '12 at 19:55
You can do quantum cryptography without entanglement. This is called a Prepare and measure scheme. In that case Alice chooses a random classical number, prepares a state accordingly and sends it to Bob. If the random generation is perfect, it is equivalent to a scheme where Alice prepare 2 entangled photons, sends one of them two Bob and measures the other? If the entangled state and the measurement are well chosen, the random result of Alice's measurement is equivalent to the random number drawn in the firs scheme. –  Frédéric Grosshans May 23 '12 at 9:25
For teleportation, one really needs entangled states to start with. –  Frédéric Grosshans May 23 '12 at 9:26

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