  Data compression is a ubiquitous aspect of modern information technology, and
the advent of quantum information raises the question of what types of
compression are feasible for quantum data, where it is especially relevant
given the extreme difficulty involved in creating reliable quantum memories. We
present a protocol in which an ensemble of quantum bits (qubits) can in
principle be perfectly compressed into exponentially fewer qubits. We then
experimentally implement our algorithm, compressing three photonic qubits into
two. This protocol sheds light on the subtle differences between quantum and
classical information. Furthermore, since data compression stores all of the
available information about the quantum state in fewer physical qubits, it
could provide a vast reduction in the amount of quantum memory required to
store a quantum ensemble, making even today's limited quantum memories far more
powerful than previously recognized.
