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arXiv:1203.1197 · Physical Review A

Distributed superdense coding over noisy channels

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

Published May 8, 2012• 29 citations
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Abstract

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.

DOI
10.1103/physreva.85.052306

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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.
We investigate the effect of noisy channels in a classical information transfer through a multipartite state which acts as a substrate for the distributed quantum dense coding protocol between several senders and two receivers. The situation is qualitatively different from the case with one or more senders and a single receiver. We obtain an upper bound on the multipartite capacity which is tightened in the case of the covariant noisy channel. We also establish a relation between the genuine multipartite entanglement of the shared state and the capacity of distributed dense coding using that state, both in the noiseless and the noisy scenarios. Specifically, we find that, in the case of multiple senders and two receivers, the corresponding generalized Greenberger-Horne-Zeilinger states possess higher dense coding capacities as compared to a significant fraction of pure states having the same multipartite entanglement.
We investigate super dense coding in the presence of noise, i.e. the subsystems of the entangled resource state have to pass a noisy unital quantum channel between the sender and the receiver. We discuss explicitly the case of Pauli channels in an arbitrary dimension and derive the super dense coding capacity (i.e. the optimal information transfer) for some given resource states. For the qubit depolarizing channel, we also optimize the super dense coding capacity with respect to the input state. We show that, below a threshold value of the noise parameter, the super dense coding protocol is optimized by a maximally entangled initial state, while above the threshold it is optimized by a product state. Finally, we provide an example of a noisy channel where non-unitary pre-processing increases the super dense coding capacity, as compared to only unitary encoding.
Quantum communication is at the heart of the quantum information theory. We study two types of quantum communication protocols over noisy transmission channels, i.e. super dense coding and cryptography protocols. In the first part of this thesis, for various scenarios, it is discussed how the super dense coding capacity is influenced by noisy quantum channels. The case of memoryless channels as well as those channels with memory which are modelled by uncorrelated and correlated noise, respectively, are considered. Explicitly Pauli channels over arbitrary dimensions are treated and the super dense coding capacity for some resource states is derived. For the qubit depolarizing channel, when noise is uncorrelated, the super dense coding capacity with respect to the input state is also optimized. This illustrates a threshold value of the noise parameter below which the super dense coding capacity is optimized by a maximally entangled initial state, while above the threshold value the super dense coding capacity is optimized by a product state. For Pauli channels, with correlated noise, the case of non unitary encoding is studied and the super dense coding capacity is derived. The first part of this thesis is concluded with an example for multipartite super dense coding. In the second part of the thesis, the problem of optimal eavesdropping on noisy states in quantum key distribution is investigated. The case of the six state protocol, when the signal states are mixed with white noise, is considered. This situation may arise either when Alice deliberately adds noise to the signal states before they leave her lab, or, in a realistic scenario when the eavesdropper (referred to as Eve) is not assumed to replace the noisy quantum channel by a noiseless one. For individual attacks, we find Eve's optimal mutual information with Alice as a function of the quantum bit error rate. Finally, the results illustrate that adding noise on the quantum level can make quantum key distribution more robust against eavesdropping.
We investigate the distributed dense coding (DC) protocol, involving multiple senders and a single or two receivers under the influence of non-Markovian noise, acting on the encoded qubits transmitted from the senders to the receiver(s). We compare the effects of non-Markovianity on DC for both the dephasing and depolarizing channels. In the case of dephasing channels, we illustrate that for some classes of states, high non-Markovian strength can eradicate the negative influence of noisy channels which is not observed for depolarizing noise. Furthermore, we incorporate randomness into the noise models by replacing the Pauli matrices with random unitaries and demonstrate the constructive impact of stochastic noise models on the quenched averaged dense coding capacity. Interestingly, we report that the detrimental effect of non-Markovian depolarizing channels in the DC protocol can be eliminated when randomness is added to the channel.