Timeline for Why can’t I use quantum teleportation to transmit data FTL 1/4 of the time?
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| May 14, 2020 at 23:12 | comment | added | Craig Gidney | @Techmaster21 If you attempt to send an N bit message via teleportation, the "every bit correct" probability will also be $2^{-1000}$. If that's still confusing you can imagine my answer saying "1 bit" instead of "1000 bits". Guessing a single bit succeeds 50% of the time, but you can clearly see that this is not a useful way to communicate a single bit. You have to do better than random guessing to transmit information. | |
| May 14, 2020 at 16:00 | comment | added | Techmaster21 | @user2723984 This is a good point, and indeed I think this is a separate question. However, I don't believe this question relies on it. I can rephrase the problem such that Alice prepares n identically prepared qubits instead, encoding an n bit message, then teleports all of them (of course this requires n pairs as well). This still shouldn't work, and perhaps this does make this answer (almost) correct. I'll think about it, edit the original question in a bit to reflect this, and then pose the approximate cloning question you suggested separately. | |
| May 14, 2020 at 15:43 | comment | added | user2723984 | @Techmaster21 the last paragraph of that post assumes you already have a large number of copies of the qubit, in which case you can reconstruct the amplitudes, but if you have a single copy you have to produce all of these clones, doing so exactly is impossible by the no-cloning theorem, and I guess (though it would be interesting to see it directly without referencing higher theorems) that any approximate cloning procedure wouldn't be enough (i.e, the error in the cloning would grow faster than the uncertainty in the amplitudes shrink) | |
| May 14, 2020 at 15:35 | comment | added | user2723984 | I think you should post "why can't I store $n$ qubits in 1 qubit and use an approximate cloning procedure to retreive the information" as a different question, as I think that's what your problem boils down to, note that I'm pretty sure such a procedure would violate Holevo's theorem, as you start from a single qubit and succesfully extract $n$ bits of information from it, even if to do it you used some other (initially "blank") qubits | |
| May 14, 2020 at 15:28 | comment | added | Techmaster21 | @user2723984 See the last paragraph of this answer physics.stackexchange.com/a/383044. I didn't intend to propose using a single-shot measurement, but rather a series of measurements on copies of the teleported qubit. | |
| May 14, 2020 at 15:18 | comment | added | user2723984 | @Techmaster21 Could you expand on how to encode 1000 bits in a single qubits and then retreive the information? (If you can do that, not only you broke multiple theorems in information theory, but you're going to collect a lot of prizes!) I guess you could encode however many bits you want in the amplitudes of the states, but you can't measure those with a single shot measurement. Maybe the problem is your proposed protocol for that. | |
| May 14, 2020 at 12:36 | comment | added | Techmaster21 | It does not succeed 50% of the time, it succeeds far less than that since the probability that all of the bits are equal to the message Alice has is (1/2)^1000 (1/2 correct * 1/2 correct * ...). Yes, 50% of the bits will be the same as the intended message, however I'm not certain that's relevant here. I could encode each of those 1000 bits in a single qubit, teleport it, and, assuming I had a way to get all of them out of that single qubit, I could have a 25% chance of getting the intended message without transmitting classical information. That's far better than random chance. | |
| May 14, 2020 at 2:58 | history | edited | Craig Gidney | CC BY-SA 4.0 |
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| May 14, 2020 at 2:51 | history | answered | Craig Gidney | CC BY-SA 4.0 |