Private Quantum Channels and the Cost of Randomizing Quantum Information
  We investigate how a classical private key can be used by two players, connected by an insecure one-way quantum channel, to perform private communication of quantum information. In particular we show that in order to transmit n qubits privately, 2n bits of shared private key are necessary and sufficient. This result may be viewed as the quantum analogue of the classical one-time pad encryption scheme. From the point of view of the eavesdropper, this encryption process can be seen as a randomization of the original state. We thus also obtain strict bounds on the amount of entropy necessary for randomizing n qubits. 
Michele Mosca (University of Waterloo), Alain Tapp (University of   Waterloo) and Ronald de Wolf (CWI and University of Amst...