  We present two new definitions of security for quantum ciphers which are
inspired by the definition of entropic security and entropic
indistinguishability defined by Dodis and Smith. We prove the equivalence of
these two new definitions. We also propose a generalization of a cipher
described by Dodis and Smith and show that it can actually encrypt n qubits
using less than n bits of key under reasonable conditions and yet be secure in
an information theoretic setting. This cipher also totally closes the gap
between the key requirement of quantum ciphers and classical ciphers.
