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Communications in Theoretical Physics

Quantum Correlations in a Two-Qubit Heisenberg XX Model under Intrinsic Decoherence

Liang Qiu

Published Oct 1, 2013• 9 citations
Publisher

Abstract

Taking into account the intrinsic decoherence, we have investigated quantum correlations in a two-qubit Heisenberg XX model when a nonuniform magnetic field is included. We compare entanglement measured by entanglement of formation, quantum discord and measurement-induced measurement (MID) and illustrate their different characteristics. Quantum discord and MID show the same features and always exist even though there is no entanglement in the long time limit. In the time evolution, quantum discord could be generated or enhanced to the stable value, while MID just decreases to the stable value.

DOI
10.1088/0253-6102/60/4/02

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Taking into account the intrinsic decoherence, we have investigated quantum correlations in a two-qubit Heisenberg XX model when a nonuniform magnetic field is included. We compare entanglement measured by entanglement of formation, quantum discord and measurement-induced measurement (MID) and illustrate their different characteristics. Quantum discord and MID show the same features and always exist even though there is no entanglement in the long time limit. In the time evolution, quantum discord could be generated or enhanced to the stable value, while MID just decreases to the stable value.
We investigate the entanglement dynamics of an anisotropic two-qubit Heisenberg XYZ system with Dzyaloshinskii-Moriya (DM) interaction in the presence of both inhomogeneity of the external magnetic field b and intrinsic decoherence which has been studied. The behavior of quantum correlation and the degree of entanglement between the two subsystems is quantified by using measurement-induced disturbance (MID), negativity (N) and Quantum Discord (QD), respectively. It is shown that in the presence of an inhomogeneity external magnetic field occur the phenomena of long-lived entanglement. It is found that the initial state is the essential role in the time evolution of the entanglement.
Quantum correlations measured by quantum discord (QD), measurement-induced distance (MID), and geometric measure of quantum discord (GMQD) in two-qubit Heisenberg XY spin chain are investigated. The effects of DM interaction and anisotropic on the three correlations are considered. Characteristics of various correlation measures for the two-qubit states are compared. The increasing D z increases QD, MID and GMQD monotonously while the increasing anisotropy both increases and decreases QD and GMQD. The three quantum correlations are always existent at very high temperature. MID is always larger than QD, but there is no definite ordering between QD and GMQD.
We investigate how thermal quantum discord (QD) and classical correlations (CC) of a two-qubit one-dimensional XX Heisenberg chain in thermal equilibrium depend on the temperature of the bath as well as on nonuniform external magnetic fields applied to two qubits and varied separately. We show that the behavior of QD differs in many unexpected ways from the thermal entanglement (EOF). For the nonuniform case ( B 1 = − B 2 ), we find that QD and CC are equal for all values of ( B 1 = − B 2 ) and for different temperatures. We show that, in this case, the thermal states of the system belong to a class of mixed states and satisfy certain conditions under which QD and CC are equal. The specification of this class and the corresponding conditions are completely general and apply to any quantum system in a state in this class satisfying these conditions. We further find that the relative contributions of QD and CC can be controlled easily by changing the relative magnitudes of B 1 and B 2 . Finally, we connect our results with the monogamy relations between the EOF, CC and the QD of two qubits and the environment.
We investigate the properties of quantum discord dynamics of a two-qubit Heisenberg XYZ system which is influenced by the environmental decoherence under an external nonuniform magnetic field. It shows that the influence of the parameters on the system heavily rely on the selection of the initial states. One point shows that the environmental decoherence cannot entirely destroy the quantum correlation, and properly controlling the parameters can inhibit the decoherence. Moreover, it presents that the inhomogeneous magnetic field cannot affect the steady quantum discord (QD), while the uniform magnetic field and the anisotropy coupling constant will change the steady QD. These investigations imply that one can obtain larger steady QD values by reasonably adjusting parameters on quantum correlation in solid state systems.
Taking the intrinsic decoherence effect into account, this paper investigates the entanglement of a two-qubit anisotropic Heisenberg XYZ model in the presence of nonuniform external magnetic fields by employing the concurrence as entanglement measure. It is found that both the intrinsic decoherence and the anisotropy of the system give a significant suppression to the entanglement. Moreover it finds that the initial state of the system plays an important role in the time evolution of the entanglement, which means that the entanglement of the system is independent of the nonuniformity and uniformity of the magnetic field when the system is in the initial state |(0)ψ = |00〉 and | ψ′ (0)〉 = m |01〉 + n |10〉, respectively.
Quantum correlation dynamics in an anisotropic Heisenberg XY Z model under decoherence is investigated by making use of concurrence C and quantum discord(QD).Firstly,we show that both the concurrence and QD exhibit oscillation with time whereas a remarkable difference between them is presented:there is an intermittently sudden phenomenon in the concurrence but not in the QD,which is valid for all the initial states of this system.Also,the interval time of entanglement sudden death is found to be strongly dependent on the initial states,the inhomogeneous magnetic field b and the anisotropic parameter ?.Then,it implies that the steady concurrence and QD can be obtained in the long-time limit,which means that the environmental decoherence cannot entirely destroy the quantum correlation,the variation of the uniform magnetic field B and the anisotropic parameter can change the magnitude of the steady concurrence and QD evidently whereas the parameter b cannot.In addition,based on the analysis of the steady concurrence and QD with t →∞,we give the reason why the magnitude of the steady concurrence and QD is so complicated with the change of the parameters B and △,whereas the parameter b is independent of the steady concurrence and QD.