Universal Compression of Ergodic Quantum Sources

Abstract

For a real number $r>0$, let $F(r)$ be the family of all stationary ergodic quantum sources with von Neumann entropy rates less than $r$. We prove that, for any $r>0$, there exists a blind, source-independent block compression scheme which compresses every source from $F(r)$ to $rn$ qubits per input block length $n$ with arbitrarily high fidelity for all large $n$. As our second result,we show that the stationarity and the ergodicity of a quantum source $\{{\rho }_m{\}}_{m=1}^{\infty }$ are preserved by any trace-preserving completely positive linear map of the tensor product form ${\mathcal{E}}^{\otimes m}$, where a copy of $\mathcal{E}$ acts locally on each spin lattice site. We also establish ergodicity criteria for so called classically-correlated quantum sources.

17 pages, minor revision