The hidden cost of quantum teleportation and remote state preparation

The amount of information transferred during standard quantum teleportation or remote state preparation is equal to the preparation information of the transmitted state, rather than the classical communication required by respective protocol. This is shown by noting that the information required to specify the operation that verifies the transmitted state is identical to the preparation information, at the given level of precision m (in bits). Depending on the resolution of the projective Hilbert space, the preparation information can be made arbitrarily precise and hence indefinitely larger than the classical communication cost. Therefore, the classical communication is insufficient to account for the transfer of preparation information, which is then attributed to the Einstein-Podolsky-Rosen channel. Some fundamental repercussions for relativistic quantum information processing are briefly discussed.