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arXiv:quant-ph/0605024

Entanglement-assisted Enhanced Information Transmission Over a Quantum Channel with Correlated Noise; A General Expression

A. Fahmi

Published May 2, 2006• 0 citations
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Abstract

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 with correlated noise and derive a general expression for the mutual information of quantum channel, for the product, maximally entangled state coding and entanglement-assisted systems with correlated noise in the Pauli quantum channels. Hence, we suggest more efficient coding in the entanglement-assisted systems for the transmission of classical information and derive a general expression for the entanglement-assisted classical capacity. Our results show that in the presence of memory, a higher amount of classical information is transmitted by two or four consecutive uses of entanglement-assisted systems.

DOI
10.48550/arxiv.quant-ph/0605024

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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.
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We study the capacity of ddd-dimensional quantum channels with memory modeled by correlated noise. We show that, in agreement with previous results on Pauli qubit channels, there are situations where maximally entangled input states achieve higher values of mutual information than product states. Moreover, a strong dependence of this effect on the nature of the noise correlations as well as on the parity of the space dimension is found. We conjecture that when entanglement gives an advantage in terms of mutual information, maximally entangled states saturate the channel capacity.
A general formula for the mutual information of the Pauli channels with memory modelled by correlated noise is derived. It is shown that the mutual information depends on the channel shrinking factor, the input state parameter and the channel memory coefficient. The analyses based on the general formula reveal that the entanglement is always a useful resource to enhance the mutual information of some Pauli channels, such as the bit flip channel and the bit-phase flip channel. Our analyses also show that the entanglement is not advantageous to the reliable transmission of classical information for some Pauli channels at any time, such as the phase flip channel and the phase damping channel.