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I have questions regarding quantum teleportation, which keep confusing me.

  1. Suppose Alice and Bob are in the same inertial frame $K$, and at time $t$ (in $K$) Alice teleports a quantum state to Bob. What I always hear is that this means that at time $t$, Bob has then got one of four states, although he does not yet know exactly which one of the four. Is this true?

  2. Now, what if Alice and Bob are both moving along the $x$-axis of $K$, in the same direction, both with the same speed $v$? If Alice does her part of the protocol at time $t$ (again, as seen in $K$), then if Bob is behind Alice (w.r.t. their common direction of movement in $K$), he must get the quantum state before $t$ in $K$, due to special relativity (as calculated by the Lorentz transformation, assuming his quantum state "arrives" at the same time as Alice sends it, in the inertial frame where both of them are at rest). This sounds weird as if the cause had happened after the effect.

  3. And what if Alice and Bob are not in the same inertial frame? Then the point in time Alice executes her part in her inertial frame does not correspond to any single point in time in Bob’s inertial frame. So what can we say about the arrival time of the quantum state to Bob?

Note: Cross-posted to Physics. I've accepted this answer there.

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  • $\begingroup$ Btw, I think the "arrival time" is well-defined, e.g. in K via the following experiment: let Alice teleport |0> at time t, and let Bob measure at time t+dt in the computational basis. Let them repeat this 100 times, where dt>0 is a small constant. Then they run another 100 times using -dt (i.e. Bob will measure before t). Using Alices's records, let them later select those cases when Bob really got |0>: they will see that during the first 100 runs Bob always got |0> as measurement result in those cases, but not during the second 100 runs. So they conclude that the "arrival time" was at dt=0. $\endgroup$
    – Tamás V
    Feb 10, 2019 at 21:21
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    $\begingroup$ Hmm, this experiment for the "arrival time" would not work, there would not be qualitative difference between the results of the first and second 100 runs. So I think the answer to my question is that there is no such thing as arrival time. But then why do the books I read talk about immediate effect on Bob's qubit? $\endgroup$
    – Tamás V
    Feb 10, 2019 at 21:45
  • $\begingroup$ Answered here: physics.stackexchange.com/questions/459986/… $\endgroup$
    – Gavin
    Jul 27, 2021 at 17:50

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Yes, Bob gets one of the four Bell states and does not know which one until he receives classical information from Alice. The state is communicated supra-luminally, that is faster than light, but the only way Bob can extract information is to apply the two bits of classical information he receives from Alice at the speed of light - not sooner. Wave function collapse does not involve the transmission of information and so it is not limited by the speed of light. This is something the Einstein, Podolsky and Rosen seem not to have appreciated in their classic paper (and in his reference to "spooky action at a distance.")

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  • $\begingroup$ One of the best explanation of spooky action on distance, +1 $\endgroup$ Nov 20, 2021 at 8:29

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