Elements of information theory
Elements of information theory
Quantum computation and quantum information
Quantum computation and quantum information
Entanglement, Quantum Phase Transitions, and Density Matrix Renormalization
Quantum Information Processing
The Data Compression Theorem for Ergodic Quantum Information Sources
Quantum Information Processing
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A system of interacting qubits can be viewed as a non-i.i.d quantum information source. A possible model of such a source is provided by a quantum spin system, in which spin-1/2 particles located at sites of a lattice interact with each other. We establish the limit for the compression of information from such a source and show that asymptotically it is given by the von Neumann entropy rate. Our result can be viewed as a quantum ana-logue of Shannon's noiseless coding theorem for a class of non-i.i.d. quantum informa-tion sources. From the probabilistic point of view it is an analog of the Shannon-McMillan-Breiman theorem considered as a cornerstone of modern Information Theory.PACS: 03.67-a; 03.67.Lx