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Prompted by the recent success in Delft, I've been reading a number of papers and articles about quantum teleportation. I'm comfortable with my understanding of most aspects but haven't found much reliable discussion about the interpretation and if anything "spooky" might be happening. Let me try to explain as clearly and concisely as I can:

A qubit obviously can't be represented with 2 classical bits, so if one can be reliably transmitted between Alice and Bob that suggests to me some spooky action at a distance involving the entanglement.

So my question is: do we have any evidence that a qubit, and not just 2 classical bits, is transmitted reliably?

I can imagine (in an overly simplified way) that Alice's apparatus actually measures her qubit and Bob's apparatus constructs a new qubit that will measure the same, using the pre-shared quantum state and the two bits.

To phrase it another way: is there some way of testing the output qubit on Bob's side which shows anything other than two bits was transmitted?

Thank you very much if you can clear this up for me. I'm not sure where else I could ask.

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If you teleport a qubit in a known state you can test whether the qubit at the end of the teleportation produces the right probabilities for measurement of some complete set of observables. There are many schemes for doing tomography on qubits, such as

http://arxiv.org/abs/1310.4492.

Also, quantum teleportation is not spooky, see

http://arxiv.org/abs/quant-ph/9906007

http://arxiv.org/abs/1109.6223.

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  • $\begingroup$ Thanks for the pointers analf, but this doesn't really help me understand. Are you saying, if Bob performs tomography on the output qubit we'll see it wasn't the once we transmitted from Alice? If the teleportation isn't spooky, it seems like only 4 possible qubits could be output for any one pre-shared state. $\endgroup$ – akvadrako Jul 1 '14 at 15:41
  • $\begingroup$ No. If Bob performs the tomography on Alice's qubit he will find that it has the same expectation values as the original, including expectation values on joint measurements with other qubits. What I meant by "not spooky" is the following: quantum mechanics is comprehensible and it doesn't involve non-locality. $\endgroup$ – alanf Jul 1 '14 at 16:03
  • $\begingroup$ So does the test show that something other than 2 bits of information were transmitted? If it does, it still looks non-local to me. $\endgroup$ – akvadrako Jul 1 '14 at 16:13
  • $\begingroup$ The information that is transmitted is quantum information that takes the form of a set of parameters describing the state of the qubit that can take on a continuous range of values: expectation values of all of the observables. In teleportation quantum information is transferred locally in a decoherent channel. There are observables that depend on the parameters that describe the state of the original qubit, but the expectation values of those observables don't depend on that information so it can't be decohered. $\endgroup$ – alanf Jul 2 '14 at 8:49
  • $\begingroup$ Thanks for the try @alanf. I would up-vote you if I could, but I just can't see how this answers my question. $\endgroup$ – akvadrako Jul 2 '14 at 10:54

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