Two-qubit Heisenberg XYZ Model Research Articles

Nonlocal correlations dynamics of two-qubit Heisenberg XYZ states with influence of intrinsic decoherence and y-component of Dzyaloshinskii-Moriya interaction

In this paper, we explore nonlocal correlation and Bell non-locality in a two-qubit Heisenberg XYZ model by using Bell-CHSH inequality and uncertainty induced nonlocality (UIN) as well as log-negativity. We consider the effects of spin-qubits XYZ-Heisenberg couplings, the y-component of DM interaction, and intrinsic decoherence. Our results show that spin-qubits Heisenberg couplings have a strong ability to create two-qubit nonlocal correlations, enhanced by combining with DM interactions. The generated Bell-CHSH nonlocality and entanglement conform to the hierarchy principle. The UIN correlation is more resistant to intrinsic decoherence compared to Bell-CHSH inequality and log-negativity. Intrinsic decoherence causes the disappearance of Bell-CHSH non-locality and log-negativity entanglement, while leading to the appearance of partial stationary spin-qubits UIN correlation.

Quantum steering vs entanglement and extracting work in an anisotropic two-qubit Heisenberg model in presence of external magnetic fields with DM and KSEA interactions

We examine the Dzyaloshinski-Moriya (DM) and Kaplan-Shekhtman-Entin-Wohlman-Aharony (KSEA) interactions in thermal equilibrium submitted to the anisotropic Heisenberg two-qubit model in an inhomogeneous magnetic field. The steerability between the two qubits is evaluated using quantum steering. The concurrence serves as a witness to quantum entanglement. Both the extracted work and the ideal efficiency of the two qubits are quantified. We discuss how quantum correlations behave in relation to the bath's temperature, the Kaplan-Shekhtman-Entin-Wohlman-Aharony coupling parameter and DM coupling. We find that the nonclassical correlations in a two-qubit Heisenberg XYZ Model are fragile under thermal effects. Nevertheless, the results indicate that the concurrence is stronger than quantum steering under thermal effects in the presence of DM and KSEA. We obtained that an extraction of work is comparable with the bare energies.

Behavior of quantum discord, local quantum uncertainty, and local quantum Fisher information in two-spin-1/2 Heisenberg chain with DM and KSEA interactions

A two-qubit Heisenberg XYZ model with Dzyaloshinsky–Moriya (DM) and Kaplan–Shekhtman–Entin-Wohlman–Aharony (KSEA) interactions is considered at thermal equilibrium. Analytical formulas are derived for the local quantum uncertainty (LQU) and local quantum Fisher information (LQFI). Using the available expressions for the entropic quantum discord, we perform a comparative study of these measures of nonclassical correlation. Our analysis showed the following: all three measures of quantum correlation have similar qualitative and even quantitative behavior on temperature for different values of system parameters, there are regions in the parameter space correspondent to a local increase of correlations with increasing temperature, and sudden changes in the behavior of quantum correlations occur at certain values of the interaction parameters.

Two-qubit Heisenberg XYZ dynamics of local quantum Fisher information, skew information coherence: Dyzaloshinskii–Moriya interaction and decoherence

We theoretically demonstrate how to achieve quantum entanglement control of a dissipative anisotropic two-qubit Heisenberg XYZ model. New dynamical features of local quantum coherence, local quantum Fisher information and Bures distance entanglement are achieved by controlling the initial state setting, DM interaction and decoherence. The proposed scheme allows for the generation of sudden changes in the entanglement. We illustrate the control by manipulating the local quantum coherence, Fisher information dynamics, and the sudden appearance of the disentanglement intervals. We further consider simultaneous changes in these behaviors for different values of the system parameters. These results provide helpful significance for understanding the dynamics of the dissipative anisotropic two-qubit Heisenberg XYZ model.

Coupled two-qubit engine and refrigerator in Heisenberg model

We have considered two-qubit Heisenberg XYZ model subject to an external magnetic field in the presence of the Dzyaloshinskii–Moriya (DM) anisotropic antisymmetric interaction as the working substance of the quantum Otto cycle. At first, a scheme is proposed for thermalization where working substance of the quantum Otto cycle is induced in the presence decoherence. The net work input and the efficiency of the engine are calculated in terms of system parameters. We investigate the effects of (DM) anisotropic antisymmetric interaction and external magnetic field on processes of the Otto cycle. An interesting phenomenon that the model reveals the mode of the cycle is a refrigerator or a heat engine. The results also enable us to determine for some values of parameters, the system is suitable for heat engine or refrigerator. Moreover, we find instances of regimes that the mode of the cycle is neither a refrigerator nor a heat engine.

Exploring the nonlocal advantage of quantum coherence and Bell nonlocality in the Heisenberg XYZ chain

The non-local advantage of quantum coherence (NAQC) is regarded as a quantum correlation, which can be reflected by the violation of a set of inequalities based on various coherence measures. In this work, we explore the NAQC and Bell nonlocality (BN) in a two-qubit Heisenberg XYZ model. The results show that one can capture the BN in the case of both anti-ferromagnetism and ferromagnetism. By contrast, the NAQC cannot be achieved in the ferromagnetism case if the magnetic field is strong. Increases of inhomogeneity and temperature give rise to reductions of the NAQC and BN, and the achievement of the NAQC at high inhomogeneity or temperatures becomes very difficult. Also, the NAQC and BN strengthen with an increase of the mean coupling coefficient. A strong mean coupling coefficient leads to the freezing of the NAQC and BN when the inhomogeneity is low. The enhancement of the magnetic field can result in the fact that the NAQC and BN experience four processes, including reduction, sudden death, revival, and reduction. Additionally, the BN is easier to capture than the NAQC. Furthermore, we focus our attention on controlling the NAQC and BN via a local filtering operation. The results demonstrate that the operation can effectively strengthen the NAQC and BN, and can also help us to control the NAQC and BN in the Heisenberg XYZ chain.

Quantum Correlation via Skew Information and Bell Function Beyond Entanglement in a Two-Qubit Heisenberg XYZ Model: Effect of the Phase Damping

In this paper, we analyze the dynamics of non-local correlations (NLCs) in an anisotropic two-qubit Heisenberg XYZ model under the effect of the phase damping. An analytical solution is obtained by applying a method based on the eigenstates and the eigenvalues of the Hamiltonian. It is observed that the generated NLCs are controlled by the Dzyaloshinskii–Moriya interaction, the purity indicator, the interaction with the environment, and the anisotropy. Furthermore, it is found that the quantum correlations, as well as the sudden death and sudden birth phenomena, depend on the considered physical parameters. In particular, the system presents a special correlation: the skew-information correlation. The log-negativity and the uncertainty-induced non-locality exhibit the sudden-change behavior. The purity of the initial states plays a crucial role on the generated nonlocal correlations. These correlations are sensitive to the DM interaction, anisotropy, and phase damping.

Dynamics of non-equilibrium thermal quantum correlation in a two-qubit Heisenberg XYZ model

The non-equilibrium thermal entanglement and quantum discord in a two-qubit Heisenberg XYZ model subjected to two thermal baths with different temperatures are investigated. The dynamical behaviors of entanglement and quantum discord under the influences of the initial states of the two-qubit system, the temperature of the thermal baths and the coupling constant $$J_z$$ are discussed. A special emphasis is devoted to study the effects of the thermal baths on the steady quantum correlation between the two qubits. Our results show that the temperature difference $$\Delta T$$ plays a key role for the appearance of steady quantum correlation, which can be enhanced by coupling constant $$J_z$$, DM interaction and non-uniform magnetic field.

Dynamics of super quantum discord and optimal dense coding in quantum channels

Quantum discord (QD), super quantum discord (SQD) and optimal dense coding at entangled states of three types of quantum channels, are investigated. The used models include: two-qubit spin squeezing, the two-qubit Heisenberg XYZ model with decoherency and the Jaynes–Cummings model. In the first two models the quantum correlations and the optimal dense coding capacity are calculated in terms of channel parameters, system initial conditions and decoherency rate. It has been found that valid dense coding can exist, although there is no trace of entanglement in the quantum channel. In contrast, despite the presence of entanglement states in the system, there may be no dense coding capacity. We investigate the effects of cavity Fock states on quantum correlations and optimal dense coding in the Jaynes–Cummings model. Cavity Fock states are found to be effective for quantum correlations and optimal dense coding. The common result of all three models is that the dynamic properties of SQD on our channel enable us to determine when and under what conditions the system is suitable for dense coding capacity.

Investigations of the Quantum Correlation in Two-Qubit Heisenberg XYZ Model with Decoherence

Quantum correlation dynamics in an anisotropic Heisenberg XYZ model under decoherence is investigated with the use of concurrence C and quantum discord (QD). With the Werner state as the initial state, we discuss the influence of mixture degree r on the dynamics. There are some difference between the time evolution behaviors of these two correlation measures with different value of r. For 0 ≤ r ≤ 1/3, there exists quantum discord but no entanglement; For 1/3<r<1, there is a ”entanglement sudden death and birth” phenomenon in the concurrence but not in the QD; For r=1, there is one interesting thing that the concurrence decays from 1 to a minimum value close to 0 but the QD vanish. In addition, we have investigated the influence of different parameters on the two correlation measures. It has been found that, the concurrence and QD both exhibit osillatory behaviors with the time evolution, which is independent on the magnetic field B and the coupling coefficient J z . However, the Dzyaloshinskii-Moriya interaction (D) and coupling coefficient J have strong influence on concurrence and QD. With the increasing of the D or J, the frequency of the oscillation getting larger. When time is fixed, with the increasing of D or J, the concurrence and QD change periodically.

Thermal quantum correlations in a two-qubit Heisenberg XYZ model with different magnetic fields

Two kinds of thermal quantum correlations, measured respectively by quantum discord (QD) and the generalized negativity (GN), are studied for various magnetic fields, couplings, and temperatures in a two-qubit Heisenberg XYZ model. It is shown that QD and GN can exhibit a similar behavior in some regions of magnetic field, coupling, and temperature, while they behave in a contrary manner in other regions. For example, QD may increase with suitable magnetic fields, couplings, and temperature when GN decreases. QD is more robust against temperature than GN, and can reveal a kink at a suitable coupling at finite temperature while GN cannot. Moreover, a nearly unchanged QD or GN can be obtained in a large region of magnetic field, coupling, and temperature. These adjustable QD and GN via the varied magnetic field, coupling, and temperature may have significant applications in quantum information processing.

Quantum correlation dynamics in a two-qubit Heisenberg XYZ model with decoherence**Project supported by the Natural Science Foundation for Young Scientists of Shanxi Province, China (Grant No. 2012021003-3) and the Special Funds of the National Natural Science Foundation of China (Grant No. 11247247).

Quantum correlation dynamics in an anisotropic Heisenberg XYZ 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 “entanglement intermittently sudden death” 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 Δ. 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 Δ, whereas the parameter b is independent of the steady concurrence and QD.

Quantum Discord Behavior about Two-Qubit Heisenberg XYZ Model with Decoherence

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.

Entanglement and Measurement-Induced Disturbance About Two-Qubit Heisenberg XYZ Model

By taking into account the nonuniform magnetic field, quantum correlation behaviors measured by concurrence and measurement-induced disturbance (MID) about a two-qubit anisotropic Heisenberg XYZ model are investigated in detail. We mainly concentrate on the differences between the entanglement and MID with the changes of different self and external control parameters. It is found that the ground state of entanglement exists the revival phenomenon, while this revival phenomenon is not included in MID. This difference is also appeared in the case of the finite temperature. Moreover, we give out the reason why the ground state entanglement and MID can behave very differently, which the former occurs the revival phenomenon whereas the latter does not. Through studying the effects about different parameters on C and MID, it presents that their magnitudes can be evidently enhanced by properly tuning B, b or adjusting the temperature. It also shows the situation which the entanglement is symmetrical with J z while MID is monotonically decreased from one constant value.

Effects of Different Spin-Spin Couplings and Magnetic Fields on Thermal Entanglement in Heisenberg XYZ Chain

The effects of spin-spin interaction on thermal entanglement of a two-qubit Heisenberg XYZ model with different inhomogeneous magnetic fields are investigated. It is shown that the entanglement is dependent on the spin-spin interaction and the inhomogeneous magnetic fields. The larger the Ji (i-axis spin-spin interaction), the higher critical value the Bi (i-axis uniform magnetic field) has. Moreover, in the weak-field regime, the larger Ji corresponds to more entanglement, while in the strong-field regime, different Ji correspond to the same entanglement. In addition, it is found that with the increase of Ji, the concurrence can approach the maximum value more rapidly for the smaller Bi, and can reach a larger value for the smaller bi (i-axis nonuniform magnetic field). So we can get more entanglement by increasing the spin-spin interaction Ji, or by decreasing the uniform magnetic field Bi and the nonuniform magnetic field bi.

Effects of Dzyaloshinski–Moriya interaction and intrinsic decoherence on teleportation via a two-qubit Heisenberg XYZ model

Quantum teleportation via the entangled channel composed of a two-qubit Heisenberg XYZ model with Dzyaloshinski–Moriya (DM) interaction in the presence of intrinsic decoherence has been investigated. We find that the initial state of the channel plays an important role in the teleported state and the average fidelity of teleportation. When the initial channel is in the state |Ψ1(0)〉 = a|00〉 + b|11〉, the average fidelity is equal to 1/3 constantly, which is independent of the DM interaction and the intrinsic decoherence effect. But when the channel is initially in the state |Ψ2(0)〉 = c|01〉 + d|10〉, the average fidelity is always larger than 2/3. Moreover, under a certain condition, the average fidelity can be enhanced by adjusting the DM interaction, and the intrinsic decoherence leads to a suppression of the fluctuation of the average fidelity.