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. 1 Introduction Secure transmission of classical information is a well studied topic. Suppose Alice wants to send an n-bit message M to Bob over an insecure (i.e. spied-on) channel, in such a way that the eavesdropper Eve cannot obtain any information about M from tapping the channel. If Alice and Bob share some secret n-bit key K, then here is a simple way for them to achieve their goal: Alice exclusive-ors M with K and sends the result M 0 = M \Phi K over the channel, Bob then xors M 0 again with K and obtains the original message M 0 \Phi K = M . Eve may see the encoded messag..