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