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.
@article{arxiv.0907.1764,
title = {Efficient compression of quantum information},
author = {Martin Plesch and Vladimir Buzek},
journal= {arXiv preprint arXiv:0907.1764},
year = {2010}
}