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We describe a universal information compression scheme that compresses anypure quantum i.i.d. source asymptotically to its von Neumann entropy, with noprior knowledge of the structure of the source. We introduce a diagonalisationprocedure that enables any classical compression algorithm to be utilised in aquantum context. Our scheme is then based on the corresponding quantumtranslation of the classical Lempel-Ziv algorithm. Our methods lead to aconceptually simple way of estimating the entropy of a source in terms of themeasurement of an associated length parameter while maintaining high fidelityfor long blocks. As a by-product we also estimate the eigenbasis of the source.Since our scheme is based on the Lempel-Ziv method, it can be applied also totarget sequences that are not i.i.d.

Universal quantum information compression and degrees of prior knowledge