Friday, 13 June 2014

How to teleport a qubit

One of the fascinating things we can do with quantum entanglement is a scheme called quantum teleportation. In the original proposal by Charlie Bennett, Gilles Brassar, Claude Crepeau, Richard Jozsa, Asher Peres and Bill Wootters, it describes a way to transmit an arbitrary quantum state between two parties who may be far apart, using only a Bell state shared between the two parties, a few qubit operations that each party can perform independently, and two bits of information that can be communicated by one party to the other.

Suppose Alice and Bob are in separate locations but they share a pair of electrons that are in the entangled state

|E) = (|u,u) + |d,d)) / sqrt(2)

where as usual |u) denotes the state of an electron having its spin pointing in the up-direction, |d) denotes that with spin in the down-direction, and |u,u) refer to the state of the first and second electrons, respectively. Let's say that Bob has the first electron on his side and Alice has the second electron on her side. 

Alice also possesses a third electron in the state

|q) = a |u) + b |d)

and she wants Bob to obtain this state. If Alice does not know what the value of a and b precisely, she can not clone the state and send a copy to Bob. However, since Alice and Bob have shared entanglement, it is possible to transfer the state of this electron into Bob's electron using teleportation, which is shown in the figure below.