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I'm reading on the Quantum Teleporation and I couldn't find anywhere what happens to the bell state qubits after the Quantum Teleporation.

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  • $\begingroup$ Hi and welcome to Quantum computing SE. Do you mean a teleported Bell state or Bell state that is part of the teleportation circuit? $\endgroup$ Jul 18 at 21:37
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    $\begingroup$ @MartinVesely I mean the two qubits of which one sent to the sender and another to the receiver. $\endgroup$
    – Malik Naik
    Jul 18 at 21:46
  • $\begingroup$ Hey Malik, it seemed I was on the right path with guessing what your question is exactly. I tried to answer it as detailed as possible. Cheers! $\endgroup$
    – DEX7RA
    Jul 18 at 22:55
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They get measured as part of the teleportation. It doesn't matter what happens to them after that. You can throw them away, reset them back to $|0\rangle$ and re-use them for something else, whatever.

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  • $\begingroup$ I like your short post! Was the last 3 hours on mine and glad we came to the same conclusion! Cheers! $\endgroup$
    – DEX7RA
    Jul 18 at 22:46
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Definitions for same starting point:

Quantum teleportation: We know that quantum teleportation is the transfer of quantum state over a distance.

Bell States: The Bell states are four specific maximally entangled quantum states of two qubits. They are in a superposition of 0 and 1 – a linear combination of the two states.


Evaluate your question:

From your question I can exclude that you are not searching an answer what "Bell state measurement" is.

But

with what happens to the bell state qubits after the Quantum Teleporation

you want to know what happens to two qubits during and after the quantum teleportation. That's a good question and luckely I can answer and break it down for you without missing any detail!


Explanatory example:

To keep this example clear, I have divided it into 3 phases

(1) The base:

You have 2 qubits in the standard basis. One is handed out to Alice (A) and the other to Bob (B). If Alice measures her qubit in the standard base she will get a perfectly random outcome. It could be 0 or 1. If Bob measures his qubit at the exact same time, the outcome would be random too BUT it will be the same as Alice has! So if Alice gets randomly a 1 then Bob has a 1 too. But only at the same time. This perfect correlation leads us to phase 2.

Summarized for simplicity: Alice and Bob share an EPR pair and each took one qubit before they became separated

(2) Quantum teleportation:

The mentioned correlation exist through the whole distance and as we know from the definition above, the changing quantum state over distance is called quantum teleportation. This correlation is very special and maybe the two particles "agreed" in advance, when the pair was created (before the qubits were separated), which outcome they would show in case of a measurement. Alice and Bob are able to measure the missing information they need.

Summarized for simplicity: Alice must deliver a qubit of information to Bob. Given Alice's measurements, Bob performs one of four operations on his half of the EPR pair and recovers the original quantum state, to get the information

(3) After quantum teleportation

The afterwards is actually not an afterwards but more like a [new] beginning. Because the information is "measured" during the quantum teleportation. The qubits can then be returned to their standard basis and thus re-used. A new exchange can take place.

Summarized for simplicity: So you can see the third phase here as getting lost in the sand. After Bob recovers the original quantum state, the qubits are ready for re-use.


Drawing

To make it more visible or clear I made a drawing to understand the 3 phases ((1),(2),(3)) I definded for explanatory example.

Explanation Drawing

Closing word:

I know this isn't an easy question and not easy to answer but I try to explain the theoretical part playful with the practical part (Bob and Alice). I hope this brought more understanding to the topic and would be happy to receive feedback!

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