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Universal Quantum Compression with Minimal Prior Knowledge

A Universal Compression scheme is presented, to compress sequences of quantum information from unknown quantum sources (i.e. described by unknown density matrix ρ) asymptotically to S(ρ), with fidelity bounded toward unity. The introduction of a“B-diagonalisation” process allows us to treat the input as if it were diagonal in a known basis B. Applying a version of the Lempel-Ziv algorithm in this basis “condenses” the sequence, leaving a tail of unentangled qubits which are then “truncated”. The rate attained depends upon the basis chosen; but we then show that the process may be repeated iteratively, to search for an optimal computational basis, and thereby compress to S(ρ) + δ qubits per signal, for any δ > 0.