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I understand that quantum teleportation fidelity is the overlap of the initial quantum state with the teleported quantum state. If the teleportation is perfect, then the fidelity would equal 1 or 100% successful of retrieving the quantum state at the desired location.

In all real experiments I've glanced at and read thoroughly, the fidelities are never 1. Doesn't this suggest that what the experimenters "teleported" was really just a different state? Doesn't the fidelity have to be exactly 1 in order to really remove a quantum state from one location and make it appear at another location?

My concern is that either I've missed something, or that we aren't really teleporting at all because the final state achieved on the other side is not equal to the initial state!

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The ontological phrasing you use to describe quantum teleportation should be a red flag. There is no sense it which the quantum state "appears". It may be the case that you are confounding the physical system itself (real, ontological) with the quantum state assigned to it by the experimenter (subjective, epistemic). In other words, think of the quantum state as the information one has about a physical system and not the physical system itself.

If the fidelity between the final state and the input is not 1, then some operation in the protocol was not perfect. Of course, this will always be the case. So, you should understand "quantum teleportation" as the protocol itself and not the act of transferring exactly the quantum state of one physical system to another. For any practical application of the protocol, it need not be perfect to be useful.

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I think I understand better now. I am fixated on the physical system itself and not the information it represents. We can still have imperfect physical state transfers, yet retain the information aspect. Therefore, it is still useful? Since the physical system is not perfectly transferred from Alice to Bob, then it would mean that the system that's "teleported" isn't really the same physical state, but a physical state that retains the important information you'd wish to transfer in Bob's hands. –  QEntanglement Mar 7 '13 at 4:18
    
Suppose Alice's physical system is a photon and the quantum state encodes the information about the polarization. Suppose Bob's physical system is an electron and the quantum state encodes information about the spin. Teleportation is a protocol by which Alice measures her photon (destroying it, say) and communicates the result to Bob. Bob does something so that the only consistent state to assign to the spin of his electron is the original state Alice assigned to her photon polarization. No "physical states" are transferred. –  Chris Ferrie Mar 7 '13 at 4:26
    
Okay, if I understand you now, you've shown an example where the two particles in the example are different, so only information is exchanged, and no physical state is transferred. It illuminates how it doesn't matter at all about physical states, all the matters here is the information transfer. I am very interested in this field of research and I am looking to apply to IQC for an internship and possibly for grad school. Could I get your email? I wish to discuss with you more about quantum information. –  QEntanglement Mar 7 '13 at 4:47
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It might also be useful to think of the following: How can we possibly verify that the teleported state is indeed equal to the initial state? We can't just look at quantum systems and know what their state is!

All that we can do is to perform measurements on a collection of systems, and from the outcomes of these measurements try to infer something about their state. But then you can see how we should be careful in interpreting the reported fidelities.

For example, the initial state may have been perfectly teleported, but it just didn't happen to be the one we thought we had prepared! But there are also other possibilities, the state may have been different for each of the measured systems, the statistical inference did not coincide with the actual state, and so forth.

In any case, as Chris pointed out, we cannot expect the teleportation protocol to ever work perfectly, but that does not imply that it is not useful to perform its intended task.

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