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Chinese Physics B

Sudden death and revival of entanglement of two qubits coupled collectively to a thermal reservoir

Xiang-Ping Liao, Jianshu Fang, Mao-Fa Fang

Published Sep 1, 2010• 7 citations
Publisher

Abstract

In this paper, we investigate the entanglement of two qubits coupled collectively to a common thermal environment and find that the the collective decay can lead to a revival of the entanglement that has already been destroyed. We also show that the ability of the system to revival entanglement relies on the mean photon number of the thermal environment and the degree of entanglement of the initial state.

DOI
10.1088/1674-1056/19/9/094203

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In this paper, we investigate the entanglement of two qubits coupled collectively to a common thermal environment and find that the the collective decay can lead to a revival of the entanglement that has already been destroyed. We also show that the ability of the system to revival entanglement relies on the mean photon number of the thermal environment and the degree of entanglement of the initial state.
We investigate the phenomenon of sudden death of entanglement in a bipartite system subjected to dissipative environments with arbitrary initial pure entangled state between two atoms. We find that in a vacuum reservoir the presence of the state where both atoms are in excited states is a necessary condition for the sudden death of entanglement. Otherwise entanglement remains for an infinite time and decays asymptotically with the decay of individual qubits. For pure 2-qubit entangled states in a thermal environment, we observe that the sudden death of entanglement always happens. The sudden death time of the entangled states is related to the temperature of the reservoir and the initial preparation of the entangled states.
We have studied the sudden death and revival of entanglement in two V-type three-level atoms coupled to the common vacuum. results show that in the case of largely separated atoms, spontaneous emission leads to decoherence and even causes entanglement sudden death. However, the excited-state decay rate of the atom can affect the time of entanglement sudden death. In the case of closely separated atoms, due to the collective effect of atoms, the entanglement which has been dead will revive in some time. The initial entanglement and the revival of entanglement arise from different causes.
We investigate the time evolution of entanglement of various entangled states of a two-qubit system exposed to either thermal or squeezed reservoirs. We show that, except for the vacuum reservoir, the sudden-death of entanglement always exists in the thermal and squeezed reservoirs. We present explicit expression for the sudden-death time of entanglement for various entangled states. We find that the sudden-death of entanglement results from the portion of the double excitation component in the initial entangled state. In this sense, the maximally entangled states of a two-qubit system that do not have the double excitation component is more robust against the quantum fluctuations of the vacuum reservoir.
We investigate the phenomenon of sudden death of entanglement in a high-dimensional bipartite system subjected to dissipative environments with an arbitrary initial pure entangled state between two fields in the cavities. We find that in a vacuum reservoir, the presence of the state where one or more than one (two) photons in each cavity are present is a necessary condition for the sudden death of entanglement. Otherwise entanglement remains for infinite time and decays asymptotically with the decay of individual qubits. For pure two-qubit entangled states in a thermal environment, we observe that sudden death of entanglement always occurs. The sudden death time of the entangled states is related to the number of photons in the cavities, the temperature of the reservoir and the initial preparation of the entangled states.
The stationary entanglement and Bell violation of two qubits collectively interacting with a common thermal reservoir is investigated, and the analytical relations among average thermal photon number of the reservoir, entanglement and Bell violation of two qubits are given in detail. The initial fraction of Bell singlet state determines whether the common thermal reservoir can enhance the entanglement of two qubits or not in this case. Moreover, the stationary maximally entangled mixed state can emerge in the collective decay of two qubits in a thermal reservoir at zero-temperature only if the fraction of Bell singlet state in the initial state is not smaller than 2/3. Furthermore, it is shown that the collective decay can induce the entanglement of two qutrits initially in the maximally mixed state, and induce distillable entanglement from bound entangled states.