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International Journal of Quantum Information

A STUDY ON THE SUDDEN DEATH AND SUDDEN BIRTH OF ENTANGLEMENT IN AN OPEN SYSTEM

YING-JIE ZHANG, Yun‐Jie Xia

Published Aug 1, 2009• 5 citations
Publisher

Abstract

In this paper, we consider the entanglement dynamics of two cavities interacting with independent reservoirs. When the cavity entanglement suddenly disappeared, the reservoir entanglement suddenly and necessarily appears. We study the effect of purity of initial entangled state of two cavities on the entanglement evolution, and acquire that the purity of initial entangled state of two cavities can control the apparition time of the entanglement sudden death and the entanglement sudden birth. Also, we find that the conditions on the apparition of the entanglement sudden death and the entanglement sudden birth can be generalized when the initial entangled state of cavities is not pure, which is a complement to the result in the paper [Phys. Rev. Lett.101 (2008) 080503] for the pure case.

DOI
10.1142/s0219749909004529

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We study the entanglement dynamics of two cavities interacting with independent reservoirs. Expectedly, as the cavity entanglement is depleted, it is transferred to the reservoir degrees of freedom. We find also that when the cavity entanglement suddenly disappears, the reservoir entanglement suddenly and necessarily appears. Surprisingly, we show that this entanglement sudden birth can manifest before, simultaneously, or even after entanglement sudden death. Finally, we present an explanatory study of other entanglement partitions and of higher dimensional systems.
In this paper, we investigate the entanglement dynamics of two entangled two-level atoms with initial X state and dipole-dipole coupling intensity in Tavis-Cummings model. The interesting phenomena of entanglement sudden death as well as sudden birth appear during the evolution process. We analyze in detail the effect of purity of initially entangled state of two atoms, the dipole-dipole coupling intensity between two atoms, and the field in the Fock state on the apparition time of entanglement sudden death and entanglement sudden birth. Furthermore, the conditions for the conversion of entanglement sudden death and entanglement sudden birth can be generalized when the initial entangled state is not pure. The results show that the above system parameters affect the concurrence, entanglement sudden birth and sudden death remarkably, the dipole-dipole coupling intensity affects amplitudes of the concurrence oscillation and leads time interval of the ESD to decrease. With the increasing of the purity, the time of entanglement sudden death and entanglement sudden birth will decrease, it is also notable that invariant and stable entanglement, which can be controlled by different initial states of the atoms, occurs for particular initial X state.
We investigate the sudden birth and sudden death of entanglement of two qubits interacting with un-correlated structured reservoirs. The system is initially prepared in two-qubit extended Werner-like state. We work out the dependence of the entanglement dynamics on both non-Markovian environments and the purity of initial state, and show that non-Markovian environments and the purity can control the time of the two-qubit entanglement sudden death and the reservoirs' entanglement sudden birth. Furthermore, under the conditions of different purity and initial entanglement, the revival of qubits' entanglement can manifest before, simultaneously or even after the disentanglement of their corresponding reservoirs.
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.
In this paper, we investigate the dynamical behaviour of entanglement in terms of concurrence in a bipartite system subjected to an external magnetic field under the action of dissipative environments in the extended Werner-like initial state. The interesting phenomenon of entanglement sudden death as well as sudden birth appears during the evolution process. We analyse in detail the effect of the purity of the initial entangled state of two qubits via Heisenberg XY interaction on the apparition time of entanglement sudden death and entanglement sudden birth. Furthermore, the conditions on the conversion of entanglement sudden death and entanglement sudden birth can be generalized when the initial entangled state is not pure. In particular, a critical purity of the initial mixed entangled state exists, above which entanglement sudden birth vanishes while entanglement sudden death appears. It is also noticed that stable entanglement, which is independent of different initial states of the qubits (pure or mixed state), occurs even in the presence of decoherence. These results arising from the combination of the extended Werner-like initial state and dissipative environments suggest an approach to control and enhance the entanglement even after purity induced sudden birth, death and revival.