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Physical Review A

Dynamics of three-qubit entanglement in photonic crystals

Jie‐Hui Huang, Zhang-Yang Chen, Tianbao Yu, Xin-Hua Deng, Jiangtao Liu, Nian-Hua Liu

Published Jan 17, 2012• 8 citations
Publisher

Abstract

The time evolution of residual entanglement in a three-qubit system embedded in a photonic crystal is investigated by using a modified conjugate gradient method. In the isotropic photonic crystal the phenomena of entanglement ``sudden death'' and entanglement ``sudden birth'' are found due to the decoherence induced by the environment and its memory effect. Compared with the environment of an isotropic photonic crystal, entanglement has a longer lifetime in the anisotropic photonic crystal if the transition frequency is near the band edge. However, once the entanglement disappears, at a finite time in the anisotropic photonic crystal, it cannot revive, which means the phenomenon of entanglement sudden birth cannot happen in the anisotropic photonic crystal. The tripartite entanglement decays faster than bipartite entanglement in both types of photonic crystal, which indicates that multipartite entanglement is more fragile than bipartite entanglement in resisting quantum noise.

DOI
10.1103/physreva.85.014301

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The time evolution of residual entanglement in a three-qubit system embedded in a photonic crystal is investigated by using a modified conjugate gradient method. In the isotropic photonic crystal the phenomena of entanglement sudden death'' and entanglement sudden birth'' are found due to the decoherence induced by the environment and its memory effect. Compared with the environment of an isotropic photonic crystal, entanglement has a longer lifetime in the anisotropic photonic crystal if the transition frequency is near the band edge. However, once the entanglement disappears, at a finite time in the anisotropic photonic crystal, it cannot revive, which means the phenomenon of entanglement sudden birth cannot happen in the anisotropic photonic crystal. The tripartite entanglement decays faster than bipartite entanglement in both types of photonic crystal, which indicates that multipartite entanglement is more fragile than bipartite entanglement in resisting quantum noise.
By applying a modified conjugate gradient method in the evaluation of three-qubit residual entanglement, the disentanglement of three-qubit states in an amplitude-damping and dephasing environment is investigated numerically. It is found that the decay of tripartite entanglement is faster than bipartite entanglement in the same qubits-noise system, which indicates that multipartite entanglement is more fragile than bipartite entanglement in resisting quantum noises. Similar to the case of a two-qubit system, three-qubit entanglement subject to an open environment may also disappear abruptly (sudden death) or decrease asymptotically, which is dependent on the conditions of the initially entangled quantum state and the properties of quantum noise.
We explore the entanglement dynamics of two qubits embedded in one-dimensional (1D) and three-dimensional (3D) photonic crystals. Our 1D results show sudden death and sudden birth of the entanglement, restricted by the initial coherence and the population in the excited state as well as the detuning. The results for the 3D crystal show entanglement death but no birth. We also discuss the entanglement of NNN qubits in the aforementioned photonic crystals.
When an initially entangled pair of qubits undergoes local decoherence processes, there are a number of ways in which the original entanglement can spread throughout the multipartite system consisting of the two qubits and their environments. Here, we report theoretical and experimental results regarding the dynamics of the distribution of entanglement in this system. The experiment employs an all optical setup in which the qubits are encoded in the polarization degrees of freedom of two photons, and each local decoherence channel is implemented with an interferometer that couples the polarization to the path of each photon, which acts as an environment. We monitor the dynamics and distribution of entanglement and observe the transition from bipartite to multipartite entanglement and back, and show how these transitions are intimately related to the sudden death and sudden birth of entanglement. The multipartite entanglement is further analyzed in terms of three- and four-partite entanglement contributions, and genuine four-qubit entanglement is observed at some points of the evolution.
The time evolution of genuine multipartite entanglement is numerically studied in a model many-spin system decohered by a structured spin bath. It is found that multipartite entanglement can be more persistent than the bipartite entanglement and can even evolve into a specific constant under certain conditions. Besides, multipartite entanglement sudden death and sudden birth are observed. It is shown that the randomness of the coupling strength and connectivity between the spins in the environment will suppress these birth and death phenomena. Furthermore, the initial state of the central system plays a significant role in determining multipartite entanglement dynamics.
Abstract We investigate the time evolution of a general two-qubit pure entangled state in different structured environments. A general expression is obtained to evaluate the entanglement dynamics of two-qubit systems for two different dissipative environments in the non-Markovian regime. In one case it is single Lorentzian and is detuned from the system while in the other case two Lorentzians form a photonic band gap and is resonant with the system. In the first case, we show that entanglement can be generated from the initial separable state in the non-Markovian regime. Compared to our earlier work under Markov approximation (Tahira et al 2008 J. Phys. B: At. Mol. Opt. Phys . 41 205501), we show that disentanglement rates as well as sudden death times are modified in structured environments. Therefore, we can retain the entanglement for a longer time by controlling the system–environment coupling parameters.