  Consider a source E of pure quantum states with von Neumann entropy S. By the
quantum source coding theorem, arbitrarily long strings of signals may be
encoded asymptotically into S qubits/signal (the Schumacher limit) in such a
way that entire strings may be recovered with arbitrarily high fidelity.
Suppose that classical storage is free while quantum storage is expensive and
suppose that the states of E do not fall into two or more orthogonal subspaces.
We show that if E can be compressed with arbitrarily high fidelity into A
qubits/signal plus any amount of auxiliary classical storage then A must still
be at least as large as the Schumacher limit S of E. Thus no part of the
quantum information content of E can be faithfully replaced by classical
information. If the states do fall into orthogonal subspaces then A may be less
than S, but only by an amount not exceeding the amount of classical information
specifying the subspace for a signal from the source.

Quantum Physics