  The standard definition of quantum state randomization, which is the quantum
analog of the classical one-time pad, consists in applying some transformation
to the quantum message conditioned on a classical secret key $k$. We
investigate encryption schemes in which this transformation is conditioned on a
quantum encryption key state $\rho_k$ instead of a classical string, and extend
this symmetric-key scheme to an asymmetric-key model in which copies of the
same encryption key $\rho_k$ may be held by several different people, but
maintaining information-theoretical security. We find bounds on the message
size and the number of copies of the encryption key which can be safely created
in these two models in terms of the entropy of the decryption key, and show
that the optimal bound can be asymptotically reached by a scheme using
classical encryption keys. This means that the use of quantum states as
encryption keys does not allow more of these to be created and shared, nor
encrypt larger messages, than if these keys are purely classical.
