Memoryless quantum information source ($\rho ={\sum }_x{p}_x|{\psi }_x⟩⟨{\psi }_x|,{\rho }^{(n)}={\rho }^{\otimes n}$)

A pure-state source emits independent states from a fixed quantum state ensemble. Its average block density operator is the tensor power of the one-use average. Unassisted reliable quantum source compression preserves the emitted quantum states, rather than only their classical labels. Schumacher compression gives the optimum asymptotic qubit rate $S(\rho )$ for such a source, with every larger rate achievable. Nonorthogonal equally likely pure states need not have entropy one: their classical labels have entropy one but their average density operator can have lower Von Neumann entropy.