10,386 research outputs found
Information transmission through a noisy quantum channel
Noisy quantum channels may be used in many information-carrying applications. We show that different applications may result in different channel capacities. Upper bounds on several of these capacities are proved. These bounds are based on the coherent information, which plays a role in quantum information theory analogous to that played by the mutual information in classical information theory. Many new properties of the coherent information and entanglement fidelity are proved. Two nonclassical features of the coherent information are demonstrated: the failure of subadditivity, and the failure of the pipelining inequality. Both properties arise as a consequence of quantum entanglement, and give quantum information new features not found in classical information theory. The problem of a noisy quantum channel with a classical observer measuring the environment is introduced, and bounds on the corresponding channel capacity proved. These bounds are always greater than for the unobserved channel. We conclude with a summary of open problems
An Upper Bound to Zero-Delay Rate Distortion via Kalman Filtering for Vector Gaussian Sources
We deal with zero-delay source coding of a vector Gaussian autoregressive
(AR) source subject to an average mean squared error (MSE) fidelity criterion.
Toward this end, we consider the nonanticipative rate distortion function
(NRDF) which is a lower bound to the causal and zero-delay rate distortion
function (RDF). We use the realization scheme with feedback proposed in [1] to
model the corresponding optimal "test-channel" of the NRDF, when considering
vector Gaussian AR(1) sources subject to an average MSE distortion. We give
conditions on the vector Gaussian AR(1) source to ensure asymptotic
stationarity of the realization scheme (bounded performance). Then, we encode
the vector innovations due to Kalman filtering via lattice quantization with
subtractive dither and memoryless entropy coding. This coding scheme provides a
tight upper bound to the zero-delay Gaussian RDF. We extend this result to
vector Gaussian AR sources of any finite order. Further, we show that for
infinite dimensional vector Gaussian AR sources of any finite order, the NRDF
coincides with the zero-delay RDF. Our theoretical framework is corroborated
with a simulation example.Comment: 7 pages, 6 figures, accepted for publication in IEEE Information
Theory Workshop (ITW
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