Universal quantum information compression and degrees of prior knowledge

Richard Jozsa, Stuart Presnell, Universal quantum information compression and degrees of prior knowledge. Proc. R. Soc. Lond. A, 459. ISSN 1364-5021, pp. 3061–3077. October 2003. No electronic version available.

Abstract

We describe a universal information compression scheme that compresses any pure quantum i.i.d. source asymptotically to its von Neumann entropy, with no prior knowledge of the structure of the source. We introduce a diagonalisation procedure that enables any classical compression algorithm to be utilised in a quantum context. Our scheme is then based on the corresponding quantum translation of the classical Lempel-Ziv algorithm. Our methods lead to a conceptually simple way of estimating the entropy of a source in terms of the measurement of an associated length parameter while maintaining high fidelity for 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 to target sequences that are not i.i.d.

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