# Quantum teleportation with moving Alice and Bob

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.

• 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. – Tamás V Feb 10 '19 at 21:21
• 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? – Tamás V Feb 10 '19 at 21:45
• I'm voting to close this question as off-topic because the OP already accepted an answer on physics.SE – glS Feb 12 '19 at 9:55
• @glS I don't think this should be closed as off-topic just because it has received an answer elsewhere. I've elaborated on my reasoning in chat. – Sanchayan Dutta Feb 12 '19 at 16:36