We show that $2n$ random classical bits are both necessary and sufficient for encrypting any unknown state of n quantum bits in an informationally secure manner. We also characterize the complete set of optimal protocols in terms of a set of unitary operations that comprise an orthonormal basis in a canonical inner product space. Moreover, a connection is made between quantum encryption and quantum teleportation that allows for a different proof of optimality of teleportation.

• Received 19 September 2002

DOI:https://doi.org/10.1103/PhysRevA.67.042317