Universal quantum information compression and degrees of prior knowledge

Abstract

We describe a universal information–compression scheme that compresses any pure quantum independent identically distributed (i.i.d.) source asymptotically to its von Neumann entropy, with no prior knowledge of the structure of the source. We introduce a diagonalization procedure that enables any classical compression algorithm to be used 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 byproduct we also estimate the eigenbasis of the source. Since our scheme is based on the Lempel–Ziv method, it can potentially be applied also to non–i.i.d. sources that satisfy some further regularity conditions.