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Canadian Journal of Physics

Dynamics of three-qubit systems in a noisy environment

NASSER METWALLY, A. Almannaei

Published Oct 29, 2015• 3 citations
Publisher

Abstract

Some properties of three-qubit systems interacting with a noisy environment are discussed. The amount of the survival entanglement is quantified for the Greenberger–Horne–Zeilinger (GHZ) and W states. It is shown that the entanglement decay depends on the noise type (correlated or non-correlated), the number of interacting qubits with the environment, and the initial state that passes through this noisy environment. In general, the GHZ state is more fragile than the W state. The phenomenon of entanglement sudden death appears in the GHZ state only for non-correlated noise.

DOI
10.1139/cjp-2015-0137

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Some properties of three-qubit systems interacting with a noisy environment are discussed. The amount of the survival entanglement is quantified for the Greenberger–Horne–Zeilinger (GHZ) and W states. It is shown that the entanglement decay depends on the noise type (correlated or non-correlated), the number of interacting qubits with the environment, and the initial state that passes through this noisy environment. In general, the GHZ state is more fragile than the W state. The phenomenon of entanglement sudden death appears in the GHZ state only for non-correlated noise.
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In practice, the interaction between quantum system and environment will lead to the decoherence of entanglement. By quantifying the entanglement through the correlation tensor, we systematically investigate the entanglement robustness of two-qubit states under the four types of noisy channels and corresponding correlated channels. We use an analytical method to find all of the most robust and fragile states under the noisy channels. The puzzling phenomenon that the most robust and fragile states have the same entanglement under noisy channels has been investigated. Moreover, we compare the entanglement robustness of a three-qubit Greenberger-Horne-Zeilinger state with a WWW state. Our method shows the behavior of entanglement under the noisy channels and characterizes the entanglement robustness of the multiqubit system analytically.
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In this paper, we investigated the dynamics of systems of two and three identical qubits interacting resonantly with a selected mode of a thermal field of a lossless resonator. We found solutions of the quantum time-dependent Liouville equation for various three- and two-qubit entangled states of qubits. Based on these solutions, we calculated the criterion of the qubit entanglement — fidelity. The results of numerical calculations of the fidelity showed that increasing the average number of photons in a mode leads to a decrease in the maximum degree of entanglement. It is shown that the two-qubit entangled state is more stable with respect to external noise than the three-qubit entangled Greenberger — Horne — Zeilinger states (GHZ). Moreover, a genuine entangled GHZ-state is more stable to noise than a GHZ-like entangled state.