"Compression of classical data is a simple procedure that allows a string of information to take up less space in a computer's memory. Given an unadulterated string of, for example, 1000 binary values, a computer could simply record the frequency of the 1s and 0s, which might require just a dozen or so binary values. Recording the information about the order of those 1s and 0s would require a slightly longer string, but it would probably still be shorter than the original sequence.
"Quantum data are rather different, and it is not possible to simply determine the frequencies of 1s and 0s in a string of quantum information. The problem comes down to the peculiar nature of qubits, which, unlike classical bits, can be a 1, a 0 or some "superposition" of both values. A user can indeed perform a measurement to record the "one-ness" of a qubit, but such a measurement would destroy any information about that qubit's "zero-ness". What is more, if a user then measures a second qubit prepared in an identical way, he or she might find a different value for its "one-ness" – because qubits do not specify unique values but only the probability of measurement outcomes."