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arXiv:1107.3591 · Physical Review A

Optimal superdense coding over memory channels

Z. Shadman, Hermann Kampermann, Dagmar Bruß, Chiara Macchiavello

Published Oct 6, 2011• 29 citations
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Abstract

We study the superdense coding capacity in the presence of quantum channels with correlated noise. We investigate both the cases of unitary and nonunitary encoding. Pauli channels for arbitrary dimensions are treated explicitly. The superdense coding capacity for some special channels and resource states is derived for unitary encoding. We also provide an example of a memory channel where nonunitary encoding leads to an improvement in the superdense coding capacity.

DOI
10.1103/physreva.84.042309

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We study the superdense coding capacity in the presence of quantum channels with correlated noise. We investigate both the cases of unitary and nonunitary encoding. Pauli channels for arbitrary dimensions are treated explicitly. The superdense coding capacity for some special channels and resource states is derived for unitary encoding. We also provide an example of a memory channel where nonunitary encoding leads to an improvement in the superdense coding capacity.
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We study multipartite superdense coding in the presence of a covariant noisy channel. We investigate the case of many senders and one receiver, considering both unitary and nonunitary encoding. We study the scenarios where the senders apply local encoding or global encoding. We show that, up to some preprocessing on the original state, the senders cannot do better encoding than local, unitary encoding. We then introduce general Pauli channels as a significant example of covariant maps. Considering Pauli channels, we provide examples for which the superdense coding capacity is explicitly determined.
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Entanglement and entanglement assisted are useful resources to enhance the mutual information of the Pauli channels, when the noise on consecutive uses of the channel has some partial correlations. In this paper, we study quantum-communication channels in ddd-dimensional systems and derive the mutual information of the quantum channels for maximally entangled states and product states coding with correlated noise. Then, we compare fidelity between these states. Our results show that there exists a certain fidelity memory threshold, which depends on the dimension of the Hilbert space (d)(d)(d) and the properties of noisy channels. We calculate the classical capacity of a particular correlated noisy channel and show that in order to achieve Holevo limit, we must use ddd particles with ddd degrees of freedom. Our results show that entanglement is a useful means to enhance the mutual information. We choose a special nonmaximally entangled state and show that in the quasiclassical depolarizing and quantum depolarizing channels, maximum classical capacity in the higher memory channels is given by the maximally entangled state. Hence, our results show that for high error channels in every degree of memory, maximally entangled states have better mutual information.