Quantum Coding Theorem for Mixed States

Details Quantum Coding Theorem for Mixed States Quantum Coding Theorem for Mixed States

1995-04-04

arxiv.org/abs/quant-ph/9504004v2

Physics

Quantum Physics

Overlap with some unpublished work noted. Limitation clarified. 11 pages, REVTEX, amsfonts

Scientific paper

We prove a theorem for coding mixed-state quantum signals. For a class of coding schemes, the von Neumann entropy $S$ of the density operator describing an ensemble of mixed quantum signal states is shown to be equal to the number of spin-$1/2$ systems necessary to represent the signal faithfully. This generalizes previous works on coding pure quantum signal states and is analogous to the Shannon's noiseless coding theorem of classical information theory. We also discuss an example of a more general class of coding schemes which {\em beat} the limit set by our theorem.

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