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Journal of Physics A Mathematical and General

Transmission rate of classical information through the thermalizing quantum channel

Masashi Ban

Published Jun 17, 2003• 1 citation
Publisher

Abstract

The transmission rate of classical information sent through the thermalizing quantum channel is considered. The entanglement-assisted capacity, the Holevo capacity and the capacity of the quantum dense coding are analytically obtained and their properties are investigated. It is found that due to the unlimited use of quantum entanglement, the entanglement-assisted capacity becomes much greater than any other capacities when the channel noise is very large and the signal power is very weak.

DOI
10.1088/0305-4470/36/26/311

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The transmission rate of classical information sent through the thermalizing quantum channel is considered. The entanglement-assisted capacity, the Holevo capacity and the capacity of the quantum dense coding are analytically obtained and their properties are investigated. It is found that due to the unlimited use of quantum entanglement, the entanglement-assisted capacity becomes much greater than any other capacities when the channel noise is very large and the signal power is very weak.
The coding theorem for the entanglement-assisted communication via infinite-dimensional quantum channel with linear constraint is extended to a natural degree of generality. Relations between the entanglement-assisted classical capacity and the χχχ-capacity of constrained channels are obtained and conditions for their coincidence are given. Sufficient conditions for continuity of the entanglement-assisted classical capacity as a function of a channel are obtained. Some applications of the obtained results to analysis of Gaussian channels are considered. A general (continuous) version of the fundamental relation between the coherent information and the measure of privacy of classical information transmission by infinite-dimensional quantum channel is proved.
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.
A coding theorem for entanglement-assisted communication via an infinite-dimensional quantum channel with linear constraints is extended to a natural degree of generality. Relations between the entanglement-assisted classical capacity and χ-capacity of constrained channels are obtained, and conditions for their coincidence are given. Sufficient conditions for continuity of the entanglement-assisted classical capacity as a function of a channel are obtained. Some applications of the obtained results to analysis of Gaussian channels are considered. A general (continuous) version of the fundamental relation between coherent information and the measure of privacy of classical information transmission via an infinite-dimensional quantum channel is proved.
Abstract A brief general review is presented of the theory of information transmission capacities of quantum communication channels, which is a development of the classical Shannon theory. Unlike a classical communication channel, a quantum channel is characterised by a whole set of different capacities, which depend on the type of transmitted information (classical or quantum) and on additional resources used during transmission. The main characteristics of a quantum channel are considered: classical capacity, capacity assisted by entanglement between the channel input and output, quantum capacity and secret classical capacity. The unique role of the quantum entanglement property, which manifests itself, in particular, in a nonclassical phenomenon of capacity superadditivity, is emphasised.
In this paper, we calculate the entanglement-assisted classical information capacity of the amplitude damping channel and compare it with the particular mutual information which is considered as the entanglement-assisted classical information capacity of this channel in Ref. 6. It is shown that the difference between them is very small. In addition, we point out that using partial symmetry and concavity of mutual information derived from the dense coding scheme, one can simplify the calculation of entanglement-assisted classical information capacities for non-unitary-covariant quantum noisy channels.