# What do we mean by teleporting state $|\psi\rangle$ through state $|\phi\rangle$?

What does it mean to teleport a state through another state? According to most of the online sources, we use a bell state for teleportation. What would be the outcome if we use any other possible state $$|\phi\rangle$$ to teleport $$|\psi\rangle$$? Would that even make sense to do?

• You have to be more specific. What sort of state do you have in mind? If it's maximally entangled then it doesn't really matter, you'll just need to change the protocol a bit. If it is not maximally entangled then your teleportation won't be perfect, but what exactly the problem is depends on what exactly the state is. Apr 19 at 14:54

As you say, it just means to replace the Bell state with the state $$|\phi\rangle$$. Of course you can do that in the protocol. Why would you want to? There are a couple of options:
• Maybe you don't have a Bell state (for example, $$|\phi\rangle$$ is your best attempt at producing a Bell state, but it's not perfect).
• If you incorporate some additional unitaries into the state $$|\phi\rangle$$, such as $$|\phi\rangle=(|0+\rangle+|1-\rangle)/\sqrt{2}$$, you can actually use the teleportation to also apply a unitary to your state. In this case, a Hadamard gate.
Answering the question in the title, the general idea is that if $$|\phi\rangle$$ is some bipartite (hopefully) entangled state, shared by two parties, call them Alice and Bob, that means that Alice and Bob's measurement results will be correlated, for many (possibly all) choice of measurements they can perform.
One can exploit such correlations to "teleport" some (local) state $$|\psi\rangle$$ from (say) Alice to Bob. To do this, Alice performs measurements after entangling her share of $$|\phi\rangle$$ with $$|\psi\rangle$$. Her measurement results thus contain some information about $$|\psi\rangle$$. But these are also correlated with Bob's measurement results. It is therefore possible, under suitable conditions, to perform some local measurement on Bob's side of the state that result in his state being identical to $$|\psi\rangle$$.