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Capacité à Zéro-Erreur des Canaux Quantiques

Abstract : In this thesis, we generalise shannon's zero-error capacity of discrete memoryless channels to quantum channels. The quantum zero-error capacity (QZEC) is defined as being the maximum amount of classical information per channel use that can be sent over a noisy quantum channel, with the restriction that the probability of error must be equal to zero. The communication protocol restricts codewords to tensor products of input quantum states, whereas collective measurements can be performed between several channel outputs. We reformulate the problem of finding the QZEC in terms of graph theory. We show that the capacity of a d-dimensional quantum channel can always be achieved by using an ensemble pure quantum states, and collective von neumann measurements are necessary and sufficient to attain the channel capacity. We discuss whether the QZEC is a non-trivial generalisation of the classical zero-error capacity. By non-trivial we mean that there exist quantum channels requiring two or more channel uses in order to reach the capacity, and the capacity can only be attained by using ensembles of non-orthogonal quantum states at the channel input. We also calculate the QZEC of some quantum channels. In particular, we exhibit a quantum channel for which we claim the QZEC can only be reached by a set of non-orthogonal states. Finally, we demonstrate that the QZEC is upper bounded by the holevo-schumacher-westmoreland capacity.
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Submitted on : Tuesday, November 16, 2010 - 3:59:13 PM
Last modification on : Friday, July 31, 2020 - 10:44:05 AM
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  • HAL Id : pastel-00004309, version 1



Rex-Antonio Da-Costa-Medeiros. Capacité à Zéro-Erreur des Canaux Quantiques. Informatique. Télécom ParisTech, 2008. Français. ⟨pastel-00004309⟩



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