What point is the entanglement lost

[trosten]

Soppuse Alice have two particles A and C that are in a partly entangled state
|Y(A,C)>. We also have another person Bob (ofcourse) with whom Alice share a pair of entangled particles D and E in the singlet state.

Now suppose Alice make a measurement on her two particles C and D, she projects their state onto the Bell basis. And send her result to Bob who performs the appropriate local operations on his particle E. That is Alice teleports the state of particle C to Bobs particle E.

Will E be entangled with A ? If not at what point is the entanglement lost between A and C (or E).

 

[trosten]

I can perhaps clarify what I mean.

To make this simpler I change the scenario a little.

Alice has the particles A anc C in the state.

|A,C> = (1/sqrt(2))(|00>+|11>)

and she has the particle D which is entangled with Bobs particle E in the similar state

|D,E> = (1/sqrt(2))(|00>+|11>)

now Alice brings particle C and D together and project their state onto the Bell basis and telephones her result to Bob. Who performs the appropriate local operations on E.

Now is A entangled with E ?

 

[slyboy]

Yes. This is called "entanglement swapping" and is the basis for proposals for constructing "quantum repeaters" http://www.arxiv.org/abs/quant-ph/9808065.