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Lecture notes in physics

Decoherence and Quantum Couplings in a Noisy Environment

Andrew J. Fisher

Published Nov 16, 2005• 0 citations
Publisher
DOI
10.1007/11526216_5

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We analyze the decoherence dynamics of a central spin coupled to a spin chain with a time-dependent noisy magnetic field, focusing on how noise influences the system's decoherence. Our results show that decoherence due to the nonequilibrium critical dynamics of the environment is amplified in the presence of uncorrelated and correlated Gaussian noise. We demonstrate that decoherence factor consistently signals the critical points, and exhibits exponential scaling with the system size, the square of noise intensity, and the noise correlation time at the critical points. We find that strong coupling between the qubit and the environment leads to partial revivals of decoherence, which diminish with increasing noise intensity or decreasing noise correlation time. In contrast, weak coupling leads to monotonic enhanced decoherence. The numerical results illustrate that, the revivals decay and scale exponentially with noise intensity. Moreover, the revivals increase and indicate linear or power law scaling with noise correlation time depending on how the correlated noise is fast or slow. Additionally, we explore the non-Markovianity of the dynamics, finding that it decays in the presence of noise but increases as the noise correlation time grows.
We propose and analyze an efficient high-dimensional quantum state transfer protocol in an XX coupling spin network with a hypercube structure or chain structure. Under free spin wave approximation, unitary evolution results in a perfect high-dimensional quantum swap operation requiring neither external manipulation nor weak coupling. Evolution time is independent of either distance between registers or dimensions of sent states, which can improve the computational efficiency. In the low temperature regime and thermodynamic limit, the decoherence caused by a noisy environment is studied with a model of an antiferromagnetic spin bath coupled to quantum channels via an Ising-type interaction. It is found that while the decoherence reduces the fidelity of state transfer, increasing intra-channel coupling can strongly suppress such an effect. These observations demonstrate the robustness of the proposed scheme.
We propose and analyze an efficient high-dimensional quantum state transfer protocol in an XX coupling spin network with a hypercube structure or chain structure. Under free spin wave approximation, unitary evolution results in a perfect high-dimensional quantum swap operation requiring neither external manipulation nor weak coupling. Evolution time is independent of either distance between registers or dimensions of sent states, which can improve the computational efficiency. In the low temperature regime and thermodynamic limit, the decoherence caused by a noisy environment is studied with a model of an antiferromagnetic spin bath coupled to quantum channels via an Ising-type interaction. It is found that while the decoherence reduces the fidelity of state transfer, increasing intra-channel coupling can strongly suppress such an effect. These observations demonstrate the robustness of the proposed scheme.