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Post-selection applied to quantum teleportation

Quantum Computing Asked on February 16, 2021

In this answer, it is stated that applying post-selection to quantum teleportation results in Alice communicating to Bob backwards in time. Could someone explain how this works?

I am particularly confused by how Alice decides what to post-select on. For example, if she wanted to teleport
$$newcommand{ket}[1]{lvert #1rangle}ket{-} = frac{1}{sqrt{2}}(ket{0}-ket{1})$$
then she could not post select on $ket{00}$ because the amplitude of this state in the first two qubits would be zero.

So, it seems like what state she post-selects on depends on what state she wants to teleport. This means she needs to tell Bob what state she is going to post-select on after deciding what state to send him. This seems equivalent to sending him the two classical bits in the usual quantum teleportation.

What am I missing here?

One Answer

As I understand it, the key caveat to postselection, at least in regards to retrocausal effects, is that Bob already knows what state Alice will post-select. Since he already knows what she will do, and she always does so with 100% success rate, then he can just treat his qubit as already having underwent the measurement and received a pure state, so that he can progress with any operations he intended to do once he had received the information immediately.

The "time travel" aspect comes into it because Bob doesn't actually need to wait for Alice to measure, so he can be said to have already received her measurement result before she made it, as she will always succeed in making it.

Answered by GaussStrife on February 16, 2021

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