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.
This paper investigates the entanglement evolution of a two-qubit anisotropic Heisenberg XYZ chain in the presence of Dzyaloshinskii-Moriya interaction. The time evolution of the concurrence is studied for the initial pure entangled states cosθ｜00〉 ＋ sinθ ｜11〉 and cos Ф ｜01〉 ＋ sin Ф10〉 at zero temperature. The influences of Dzyaloshinskii Moriya interaction D, anisotropic parameter △ and environment coupling strength γ on entanglement evolution are analysed in detail. It is found that the effect of noisy environment obviously suppresses the entanglement evolution, and the Dzyaloshinskii-Moriya interaction D acts on the time evolution of entanglement only when the initial state is cos Ф ｜01〉 sinФ｜10〉. Finally, a formula of steady state concurrence is obtained, and it is shown that the stable concurrence, which is independent of different initial states and Dzyaloshinskii-Moriya interaction D, depends on the anisotropic parameter △ and the environment coupling strength.
By analysing the properties of two-mode quadratures in an entangled state representation （ESR） we derive from ESR some complicated exponential quadrature operators for nonlinear two-mode squeezing, which directly leads to wave function of the nonlinear squeezed state in ESR.
