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Information Capacities of Spin Chains

Vittorio Giovannetti, Rosario Fazio

Published Jan 1, 2004• 0 citations
OpenAlex

Abstract

Information capacities are used to characterize the quantum correlations in unmodulated spin chains. By studying the qubit amplitude damping channel, we calculate the quantum capacity Q, the entanglement assisted capacity C_E, and the classical capacity C_1 of a spin chain with ferromagnetic Heisenberg interactions.

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Information-capacity description of spin-chain correlations

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Information capacities achievable in the multi-parallel-use scenarios are employed to characterize the quantum correlations in unmodulated spin chains. By studying the qubit amplitude damping channel, we calculate the quantum capacity $Q$, the entanglement assisted capacity ${C}_{E}$, and the classical capacity ${C}_{1}$ of a spin chain with ferromagnetic Heisenberg interactions.

arXiv:quant-ph/0405110•Physical Review A•Mar 15, 2005•147 citations

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Information capacities achievable in the multi-parallel-use scenarios are employed to characterize the quantum correlations in unmodulated spin chains. By studying the qubit amplitude damping channel, we calculate the quantum capacity QQQ, the entanglement assisted capacity CE{C}_{E}CE​, and the classical capacity C1{C}_{1}C1​ of a spin chain with ferromagnetic Heisenberg interactions.
The primary objective of quantum Shannon theory is to evaluate the capacity of quantum channels. In spite of the existence of rigorous coding theorems that quantify the transmission of information through quantum channels, superadditivity effects limit our understanding of the channel capacities. In this paper, we mainly focus on a family of channels known as multilevel amplitude damping channels. We investigate some of the information capacities of the simplest member of the multilevel amplitude damping channel, a qutrit channel, in the presence of correlations between successive applications of the channel. We find the upper bounds of the single-shot classical capacities and calculate the quantum capacities associated with a specific class of maps after investigating the degradability property of the channels. Additionally, the quantum and classical capacities of the channels have been computed in entanglement-assisted scenarios.
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.
Abstract Evaluating capacities of quantum channels is the first purpose of quantum Shannon theory, but in most cases the task proves to be very hard. Here, we introduce the set of Multi-level Amplitude Damping quantum channels as a generalization of the standard qubit Amplitude Damping Channel to quantum systems of finite dimension d . In the special case of d = 3, by exploiting degradability, data-processing inequalities, and channel isomorphism, we compute the associated quantum and private classical capacities for a rather wide class of maps, extending the set of models whose capacity can be computed known so far. We proceed then to the evaluation of the entanglement assisted quantum and classical capacities.