  We propose a scheme for an exact efficient transformation of a tensor product
state of many identically prepared qubits into a state of a logarithmically
small number of qubits. Using a quadratic number of elementary quantum gates we
transform N identically prepared qubits into a state, which is nontrivial only
on the first log(N+1) qubits. This procedure might be useful for quantum
memories, as only a small portion of the original qubits has to be stored.
Another possible application is in communicating a direction encoded in a set
of quantum states, as the compressed state provides a high-effective method for
such an encoding.
