C above is used only to distinguish this state from A and B, below. Next, the protocol requires that Alice and Bob share a maximally entangled state. This state is fixed in advance, by mutual agreement between Alice and Bob, and can be any one of the four Bell states shown. It does not matter which one. , , . , In the following, assume that Alice and Bob share the state Alice obtains one of the particles in the pair, with the other going to Bob. (This is implemented by preparing the particles together and shooting them to Alice and Bob from a common source.) The subscripts A and B in the entangled state refer to Alice's or Bob's particle. At this point, Alice has two particles (C, the one she wants to teleport, and A, one of the entangled pair), and Bob has one particle, B. In the total system, the state of these three particles is given by Alice will then make a local measurement in the Bell basis (i.e. the four Bell states) on the two particles in her possession. To make the result of her measurement clear, it is best to write the state of Alice's two qubits as superpositions of the Bell basis. This is done by using the following general identities, which are easily verified: and After expanding the expression for , one applies these identities to the qubits with A and C subscripts. In particular,and the other terms follow similarly. Combining similar terms, the total three particle state of A, B and C together becomes the following four-term superposition: Note that all three particles are still in the same total state since no operations have been performed. Rather, the above is just a change of basis on Alice's part of the system. The actual teleportation occurs when Alice measures her two qubits A,C, in the Bell basis Equivalently, the measurement may be done in the computational basis, , by mapping each Bell state uniquely to one of with the quantum circuit in the figure to the right. Given the above expression, evidently the result of Alice's (local) measurement is that the three-particle state would collapse to one of the following four states (with equal probability of obtaining each): Alice's two particles are now entangled to each other, in one of the four Bell states, and the entanglement originally shared between Alice's and