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The design of error-correcting codes used in modern communications relies on information theory to quantify the capacity of a noisy channel to send information [1].
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Winter, A., The maximum output p-norm of quantum channels is not multiplicative for any p > 2 p>2 , arXiv.org:0707.0402
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G. Smith and J. Yard, Quantum Communication with Zero-Capacity Channels, Science 321
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Hayden, P. and Winter, A., Counterexample to the maximal p-norm multiplicativity conjecture for all p > 1 p>1 , arXiv.org:0807.4753
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Cubitt, T., Harrow, A. W., Leung, D., Montanero, A., and Winter, A., Counterexamples to additivity of minimum output p-Renyi entropy for p close to 0, arXiv.org:0712.3628
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Hastings, M. B., Random Unitaries Give Quantum Expanders, Phys. Rev. A 76
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Ben-Aroya, A. and Ta-Shma, A., Quantum Expanders and the Quantum Entropy Difference Problem, arXiv:quant-ph/0702129
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