Studying quantum correlation dynamics of a central two-qubit system coupled to Ising chain model, we obtain that the evolution of quantum discord and geometric measure of quantum discord for the central atoms. We find that quantum correlation exists a sudden transition in the weak coupled interaction near the quantum critical point of Ising chain. Moreover, the evolution of geometric measure of quantum discord in invariant to some extent.
Studying quantum correlation dynamics of a central two-qubit system coupled to Ising chain model, we obtain that the evolution of quantum discord and geometric measure of quantum discord for the central atoms. We find that quantum correlation exists a sudden transition in the weak coupled interaction near the quantum critical point of Ising chain. Moreover, the evolution of geometric measure of quantum discord in invariant to some extent.
The quantum coherence and correlation dynamics for a two-qubit system in the Ising spin-chain environment are studied. A sudden change of coherence is found near the critical point, which provides us with an effective way to detect the quantum phase transition. By studying the relationship between quantum discord and coherence, we find that coherence displays the behavior of classical correlation for t < t 0 , and of quantum discord for t > t 0 , where t 0 is the time-point of a sudden transition between classical and quantum decoherence.
Quantum coherence has played a decisive role in quantum information processing. On the other hand, quantum correlation can be considered as a powerful resource for delivering quantum information. Both quantum coherence and quantum correlation may occur in an information propagating process, which challenges us to understand the relationship between coherence and correlation. This is also an important procedure for physicists to know the features of quantum resources. Any quantum system interacting with its surrounding environment will destroy the quantum coherence and fail to fulfil any task of delivering quantum information. In this sense, studying the dynamics of quantum correlation and quantum coherence is very fascinating. In this paper, we investigate the dynamics of the quantum correlation and quantum coherence for two central qubits coupled to their own spin baths modeled by the XY spin chain with Dzyaloshinsky-Moriya interaction. We employ the quantum discord to characterize the quantum correlation, and use the relative entropy to measure quantum coherence. In this way the evolution law of the quantum discord and the relative entropy of quantum coherence of two-qubit system are derived, and the evolution law depends not only on the Dzyaloshinsky-Moriya interaction, the anisotropy parameter and the total number of spin chain sites, but also on the coupling strength between the central spin and its spin chain. Our findings are as follows. Firstly, we find that near the critical point of spin chain the quantum coherence abruptly changes, which can be used to detect the existence of quantum phase transition. Secondly, at the critical point, the relative entropy of quantum coherence is the same as that of classical correlation when time tt0, and it is the same as that of quantum discord when time tt0. At time t0, the sudden transition from quantum discord to classical correlation occurs. All in all, the relative entropy of quantum coherence reflects the behaviors of classical correlation and quantum discord for times tt0 and tt0, respectively, which is caused by the change of the optimal basis for quantum discord. Thirdly, the dynamics of quantum correlation and quantum coherence keep invariant under the scaling variation of the total number of spin chain sites and the coupling strength. Moreover, we find that all the Dzyaloshinsky-Moriya interactions and the anisotropy parameters, as well as the coupling strengths will enhance the decay of quantum coherence and quantum correlation, while they have no obvious effect on the relationship between dynamics of coherence and correlation. The above discussion reveals some new features of quantum coherence and quantum correlation, which may be useful in further developing quantum information theory.
We investigate the dynamic behaviors of quantum discord for a central two-qubit system coupled to an XY-spin-chain environment. In the weak-coupling regime, we show that the quantum discord for the two central qubits can become minimized rapidly close to the critical point of a quantum phase transition. By considering the two qubits that are initially prepared in the Werner state, we study the evolution of the quantum discord and that of entanglement under the same conditions. Our results imply that entanglement can disappear completely after a finite time, while the quantum discord decreases and tends to be a stable value according to the initial-state parameter for a very-long-time interval. In this sense, the quantum discord is more robust than entanglement for the quantum system exposed to the environment. The relation between the quantum correlations and the classical correlation is also shown for two particular cases.
We study quantum discord induced by a quantum-critical environment. Two spin halves are independently coupled to the common environment which is modelled by the Ising spin chain in a transverse field. During the time evolution, non-zero discord is induced whereas entanglement cannot be induced due to the special initial state chosen by us. For some cases we analytically obtain quantum discord and its geometric measure. From the numerical results, one can observe that induced quantum discord increases quickly from zero to a steady value when the environment approaches the critical point. Moreover, induced discord may reach its maximum close to the critical point. The special phenomena of induced discord can be used to indicate quantum criticality. We also consider another environment modelled by the spin-1/2 XX chain with three-spin interaction, which also displays second-order quantum phase transition.
We study the dynamics of quantum discord (QD) of two qubits independently coupled to an Ising spin chain in a transverse field, which exhibits a quantum phase transition. For this model, we drive the corresponding Kraus operators, obtain the analytic results of QD and compare the dynamics of QD with the dynamics of relative entropy of entanglement nearby the critical point. It is shown that the impact of the quantum criticality environment on QD can be concentrated in a very narrow region nearby the critical point, so it supplies an efficient way to detect the critical points. In the vicinity of the critical point, the evolution of QD is shown to be more complicated than that of entanglement. Furthermore, we find that separable states can also be used to reflect the quantum criticality of the environment.
In this paper, we study the dynamical processes of quantum coherence and correlations for two central qubits system coupled with a transverse Ising spin chain. Suppose the initial state of quantum system is the Werner state and the initial state of environment is the ground state of spin chain, and the corresponding time evolution operator, decoherence factor and reduced density matrix are given. We deduce the analytical expressions of evolution of quantum coherence, entanglement and quantum discord. We find that when the spin chain undergoes quantum phase transition (QPT), the entanglement vanished at time [Formula: see text], and the coherence and discord vanished when the decoherence factor decayed to zero. Besides, we also find that the environmental scale N, coupling strength g and parameter P of Werner state do not change the evolution rules of quantum correlation, but accelerate their decay rate with these parameters’ increase.