 What is extraordinary about this phenomenon is that Alice and Bob have managed to use their shared entangled state as a quantum communication channel to destroy the state \(\ket{u}\) of a photon in Alice’s part of the universe and recreate it in Bob’s part of the universe. Since the linear polarization state of a photon requires specifying a direction in space (the value of an angle that can vary continuously), without a shared entangled state Alice would have to convey an infinite amount of classical information to Bob for Bob to be able to reconstruct the state \(\ket{u}\) precisely. The amount of classical information associated with a binary alternative, represented as 0 or 1, where each alternative has equal probability, is one binary digit or ‘bit.’ To specify an arbitrary angle as a decimal requires an infinite sequence of digits between 0 and 9, or an infinite sequence of 0s and 1s in binary notation. The outcome of Alice’s operation, which has four possible outcomes with equal probability of 1/4, can be specified by two bits of classical information. Remarkably, Bob can reconstruct the state \(\ket{u}\) on the basis of just two bits of classical information communicated by Alice, apparently by exploiting the entangled state as a quantum communication channel to transfer the remaining information. For further discussion of quantum teleportation, see Nielsen and Chuang 2000, or Richard Josza’s article “Quantum Information and its Properties” in Lo, Popescu, and Spiller 1998.