Quantum Teleportation - Motivation

Motivation

Suppose Alice has a qubit in some arbitrary quantum state . (A qubit may be represented as a superposition of states, labeled and .) Assume that this quantum state is not known to Alice and she would like to send this state to Bob. Ostensibly, Alice has the following options:

1. She can attempt to physically transport the qubit to Bob.
2. She can broadcast this (quantum) information, and Bob can obtain the information via some suitable receiver.
3. She can perhaps measure the unknown qubit in her possession. The results of this measurement would be communicated to Bob, who then prepares a qubit in his possession accordingly, to obtain the desired state. (This hypothetical process is called classical teleportation.)

Option 1 is highly undesirable because quantum states are fragile and any perturbation en route would corrupt the state.

Option 2 is forbidden by the no-broadcast theorem.

Option 3 (classical teleportation) has also been formally shown to be impossible. (See the no teleportation theorem.) This is another way to say that quantum information cannot be measured reliably.

Thus, Alice seems to face an impossible problem. A solution was discovered by Bennett, et al. The components of a maximally entangled two-qubit state are distributed to Alice and Bob. The protocol then involves Alice and Bob interacting locally with the qubit(s) in their possession and Alice sending two classical bits to Bob. In the end, the qubit in Bob's possession will be in the desired state.