# How can a correlation be teleported?

I am aware of how a qubit can be teleported from party $A$ to party $B$ if both the parties are entangled. Is there a similar way to teleport a correlation? I googled and found Entanglement Teleportation via Werner States. But it also talks about noisy channels, which I am not well acquainted with. Is this the only way or is there a simple protocol?

• What exactly do you mean by "teleporting a correlation"? What exactly is "a correlation" in this context? – ACuriousMind May 18 '15 at 15:39
• I meant to ask , if I have an entangled state and I want to teleport it from party $A$ to party $B$ which themselves are entangled is it similar to teleporting a simple qubit ? – sashas May 18 '15 at 15:53
• You might want to look into quantum repeaters, designed to introduce entanglement (=correlations) between very distant parties by using intermediary parties and teleporation. – Martin May 18 '15 at 16:31

You can use the teleportation protocol to teleport and part of a larger quantum state (which can be arbitrarily entangled), and it will work the way it should: I.e., if initially A+C hold $\vert\psi\rangle_{AC}$, after the protocol B+C hold $\vert\psi\rangle_{BC}$. The same is true if the initially shared state is mixed. This follows from the linearity of teleportation.

I was under the impression that the standard teleportation protocol preserves teleportation. That is to say that if Alice shares some entangled state with Bob, and then teleports her part of this state to Carol in the usual way, Carol will now share that entangled state with Bob.

Using this teleportation protocol requires Alice and Carol to share a maximally entangled state for each qubit they wish to teleport between each other. The paper you found is looking at the case where they share less than maximally entangled states.