Heisenberg XYZ Chain Research Articles

Quantum teleportation in Heisenberg chain with magnetic-field gradient under intrinsic decoherence

One of the most appealing quantum communication protocols is quantum teleportation, which involves sharing entanglement between the sender and receiver of the quantum state. We address the two-qubit quantum teleportation based on the Heisenberg XYZ chain with a magnetic-field gradient affected by intrinsic decoherence. An atomic spin chain is primarily coupled to the linear gradient of the magnetic field in the x-direction, with the assumption that the magnetic field varies linearly with the position of the atom. By using the concepts of fidelity and average fidelity in the presence of the magnetic field gradient and under the effect of intrinsic decoherence in the current model, and considering the variables of the system, an improved quantum teleportation can be achieved. In addition, using the concept of remote quantum estimation, we examine remote quantum sensing in this article, which is very useful in quantum communication.

Exploring quantum correlations of two-qubit Heisenberg chain model influenced by magnetic dipole–dipole, magnetic field, and a symmetric cross interaction

The concepts of concurrence, 3-steerability, and Clauser–Horne–Shimony–Holt (CHSH) inequality are employed to investigate the environmental impacts on the quantum correlations of the two-spin-1/2 Heisenberg XYZ chain model. In particular, the effects of a homogeneous magnetic field, symmetric cross interaction, and dipole–dipole interaction on the entanglement, degree of steerability, and non-locality are discussed. Results show that the entanglement and steering phenomena are bounded by the non-locality for both positive and negative values of dipole–dipole coupling. It has also been observed that higher symmetric cross-interaction strengthens the quantum correlations, whereas the homogeneous magnetic field weakens the quantumness of the system. The findings indicate that a magnetic field normal to the magnetic dipole yields better quantum correlations than when they are parallel.

Thermal Fisher and Wigner–Yanase information correlations in two-qubit Heisenberg XYZ chain

Using Wigner–Yanase and Fisher information [including local quantum uncertainty (LQU) and local quantum Fisher information (LQFI)] as well as log-negativity, we investigate the thermal non-local correlations of two-qubit Heisenberg XYZ non-X states produced in the presence of the Dzyaloshinskii–Moriya (DM) interaction. The two-spin XYZ-Heisenberg non-local correlation decay can be weakened by increasing the DM interaction as well as the spin–spin XYZ-Heisenberg interactions. The LQFI correlation has greater resistance to thermal degradation. The spin–spin y-component antiferromagnetic coupling has a higher ability to protect the generated spin–spin nonlocal correlations against high temperatures. The emergence of the phenomena of the sudden death of log-negativity and the sudden change of the LQFI and LQU depend on the spin–spin XYZ-Heisenberg and DM interactions as well as on the bath temperature. The generated asymmetric correlations resulting due to the x,y-component spin interactions confirm that the antiferromagnetic coupling has a high ability to generate a maximally correlated two-qubit state. While the generated correlations, due to two-spin z-component interaction, present symmetric dynamics, and its amount depends on the x-component spin interaction.

Influence of Dzyaloshinskii–Moriya and Kaplan–Shekhtman–Entin–Wohlman–Aharony interactions on quantum entanglement in a two-qubit Heisenberg XYZ chain

Influence of Dzyaloshinskii–Moriya and Kaplan–Shekhtman–Entin–Wohlman–Aharony interactions on quantum entanglement in a two-qubit Heisenberg XYZ chain

Entangled quantum refrigerator based on two anisotropic spin-1/2 Heisenberg XYZ chain with Dzyaloshinskii–Moriya interaction

A quantum refrigerator based on anisotropic two spin-1/2 Heisenberg XYZ model in external magnetic fields with Dzyaloshinski–Moriya (DM) interaction is suggested. It consists of establishing different expressions of efficiency and thermodynamic quantities as a function of the homogeneous magnetic fields $$B_z$$ and the DM interaction ( $$D_z$$ ). A multipartite concurrence is employed as a measure of thermal entanglement in order to investigate the relationship between the entanglement and thermodynamic quantities. Many particular results related to variations in the coupling constants of the system are shown. However, the results ensure that a variation of the coupling constants has a significant impact on the results of the suggested system. All these investigations are established with respect to the conservation of the second law of thermodynamics.

Quantum Fisher Information of a Teleported State in Heisenberg XYZ Chain With Magnetic Field and Kaplan–Shekhtman–Entin-Wohlman–Aharony Interaction

One of the teleportation versions is applied to convey an entangled two-qubit system via a class of a two-qubit XYZ Heisenberg chain model. At thermal equilibrium, the exact solution of the XYZ model with an external magnetic field and the Kaplan-Shekhtman-Entin-Wohlman-Aharony interaction (KSEWA-interaction) is proposed in X, and Z direction. The teleported quantum Fisher information is studied, where we estimate the weight parameter θ, temperature and the strength parameter of KSEWA-interaction. It is found that, the strength of the KSEWA-interaction and the magnetic field be of benefit in the case of estimating the weight function. Meanwhile, the temperature decreases the teleported information.

Local quantum Fisher information and local quantum uncertainty in two-qubit Heisenberg XYZ chain with Dzyaloshinskii–Moriya interactions

Quantum correlations play an important role in quantum information theory. Quantum Fisher information (QFI) via local observables and via local measurements (i.e. local QFI (LQFI)) is a fundamental concept in quantum estimation and quantum metrology. LQFI captures the quantumness of correlations in a multicomponent quantum system. This new discord-like measure is very similar to the quantum correlations measure called local quantum uncertainty (LQU). In this work we will study the LQFI and the LQU in the two-qubit Heisenberg XYZ spin chain model with Dzyaloshinskii–Moriya (DM) interaction in the z-direction. Here we show that the DM interaction and spin interactions along the x- and z-axes can increase and maintain LQFI and LQU. It is also shown that because of thermal fluctuations LQFI and LQU are decreased by increasing temperature. They are equal to one at very low temperature and start to decay only after a thereshold temperature.

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.

Criticality and factorization in the Heisenberg chain with Dzyaloshinskii-Moriya interaction

In this work, we address the ground state properties of the anisotropic spin-1/2 Heisenberg XYZ chain under the interplay of magnetic fields and the Dzyaloshinskii-Moriya (DM) interaction which we interpret as an electric field. The identification of the regions of enhanced sensitivity determines criticality in this model. We calculate the Wigner-Yanase skew information (WYSI) as a coherence witness of an arbitrary two-qubit state under specific measurement bases. The WYSI is demonstrated to be a good indicator for detecting the quantum phase transitions. The finite-size scaling of coherence susceptibility is investigated. We find that the factorization line in the antiferromagnetic phase becomes the factorization volume in the gapless chiral phase induced by DM interactions, implied by the vanishing concurrence for a wide range of field. We also present the phase diagram of the model with three phases: antiferromagnetic, paramagnetic, and chiral, and point out a few common mistakes in deriving the correlation functions for the systems with broken reflection symmetry.

Quantum-memory-assisted entropic uncertainty in two-qubit Heisenberg XYZ chain with Dzyaloshinskii–Moriya interactions and effects of intrinsic decoherence

Quantum-memory-assisted entropic uncertainty relation (QMA-EUR) in two-qubit Heisenberg XYZ spin chain model with Dzyaloshinskii–Moriya (DM) interaction has been investigated. The paper shows that the DM interactions and the spin interactions alone x, y, z directions can efficiently suppress the entropic uncertainty of Pauli observables ( $$\sigma _{x}$$ and $$\sigma _{z}$$ ), even make the entropic uncertainty close to zero. As well, it is pointed out that the entropic uncertainty reaches to zero at very low temperature, starts to increase with temperature after a threshold, and generally becomes constant at a fixed value. We also verified the Bob’s uncertainty about Alice’s measurement outcomes is anticorrelated with the sum of the accessible information of observer. Furthermore, the decoherence conditions including dephasing and noisy environments are considered. For the fixed initial state, the entropic uncertainty of the XYZ model with DM interaction in z-direction are independent of spin–spin coupling $$J_z$$ and the anisotropy parameter $$\varDelta $$ . In the dephasing environment, the evolutions of entropic uncertainty and its lower bound $$U_{B}$$ oscillate with the time and saturates at a finite value, and this value is varied with the purity parameter r of initial state. In the noisy environment, the entropic uncertainty and its lower bound monotonically increase with the time and will be stable at value 2 quickly. This is because the combined effects of the DM interaction and the decoherence force the various initial entanglement states to oscillate into an identical state, regardless of the value of $$D_{z}$$ and the parameter r of initial state.

Quantum Dense Coding About a Two-Qubit Heisenberg XYZ Model

By taking into account the nonuniform magnetic field, the quantum dense coding with thermal entangled states of a two-qubit anisotropic Heisenberg XYZ chain are investigated in detail. We mainly show the different properties about the dense coding capacity (χ) with the changes of different parameters. It is found that dense coding capacity χ can be enhanced by decreasing the magnetic field B, the degree of inhomogeneity b and temperature T, or increasing the coupling constant along z-axis J z . In addition, we also find χ remains the stable value as the change of the anisotropy of the XY plane Δ in a certain temperature condition. Through studying different parameters effect on χ, it presents that we can properly turn the values of B, b, J z , Δ or adjust the temperature T to obtain a valid dense coding capacity (χ satisfies χ > 1). Moreover, the temperature plays a key role in adjusting the value of dense coding capacity χ. The valid dense coding capacity could be always obtained in the lower temperature-limit case.

Quantum-memory-assisted entropic uncertainty relation in a Heisenberg XYZ chain with an inhomogeneous magnetic field

The uncertainty principle provides a nontrivial bound to expose the precision for the outcome of the measurement on a pair of incompatible observables in a quantum system. Therefore, it is of essential importance for quantum precision measurement in the area of quantum information processing. Herein, we investigate quantum-memory-assisted entropic uncertainty relation (QMA-EUR) in a two-qubit Heisenberg spin chain. Specifically, we observe the dynamics of QMA-EUR in a realistic model there are two correlated sites linked by a thermal entanglement in the spin chain with an inhomogeneous magnetic field. It turns out that the temperature, the external inhomogeneous magnetic field and the field inhomogeneity can lift the uncertainty of the measurement due to the reduction of the thermal entanglement, and explicitly higher temperature, stronger magnetic field or larger inhomogeneity of the field can result in inflation of the uncertainty. Besides, it is found that there exists distinct dynamical behaviors of the uncertainty for ferromagnetism and antiferromagnetism chains. Moreover, we also verify that the measuring uncertainty is dramatically anti-correlated with the purity of the bipartite spin system, the greater purity can result in the reduction of the measuring uncertainty, vice versa. Therefore, our observations might provide a better understanding of the dynamics of the entropic uncertainty in the Heisenberg spin chain, and thus shed light on quantum precision measurement in the framework of versatile systems, particularly solid states.

Quantum correlations in a two-qubit anisotropic Heisenberg XYZ chain with uniform magnetic field

Quantum correlations in an anisotropic Heisenberg XYZ chain is investigated by use of concurrence C and measurement-induced disturbance (MID). We show that the behaviors of the MID are remarkably different from the concurrence. Firstly, it is shown that there is a revival phenomenon in the concurrence but not in the MID, which is suitable for both the ground state case and the finite temperature case. Based on the analysis of the ground-state C and MID structures, we illustrate the reason why the ground-state MID does not show a revival phenomenon in detail. Then we explore different effects of the external and self parameters on entanglement and MID behaviors. It can be shown that the region of MID is evidently larger than the case of concurrence, and that the concurrence signals a quantum phase transition even at finite T while MID does not. Cases where the concurrence finally maintains one nonzero constant value regardless of the value of the variable B for a constant Jz, while MID decreases monotonously to zero with increasing B. We also show that if B can take a proper range of values, the concurrence decreases with the improvement of the anisotropic parameter γ, whereas an opposite effect for MID behaviors is presented.

Quantum teleportation via two-qubit Heisenberg XYZ chain

Quantum teleportation via the entanglement channel composed of a two-qubit Heisenberg XYZ chain with Dzyaloshinskii–Moriya interaction in the presence of both inhomogeneous external magnetic field and intrinsic decoherence has been investigated. It is shown that the initial state of the channel plays an important role in the fully entangled fraction and the average fidelity of teleportation. It is found that when the initial system is in the entangled state |Ψ⟩ = m2|01⟩ + n2|10⟩ the corresponding average fidelity is always larger than 2/3.

Effects of inhomogeneous magnetic fields and different Dzyaloshinskii-Moriya interaction on entanglement and teleportation in a two-qubit Heisenberg XYZ chain

In this paper we calculate the thermal entanglement and teleportation in a two-qubit Heisenberg XYZ chain with the different Dzyaloshinskii-Moriya interaction and inhomogeneous magnetic fields. The analytical expressions of the concurrence and the average fidelity are obtained for this model. We have shown that the quantum phase transition occurs in the system and the quantum phase transition point depends on the inhomogeneity of magnetic fields. We compare the x-component Dzyaloshinskii-Moriya interaction with the z-component Dzyaloshinskii-Moriya interaction on the effects of quantum teleportation. It is found that we can take Dzyaloshinskii-Moriya interaction as one of the effective control parameters for the teleportation manipulation.

Steady Quantum Discord Behavior for Two Qubits Heisenberg XYZ Chain with Intrinsic Decoherence

By taking into account the intrinsic decoherence and the nonuniform magnetic field, quantum discord (QD) and steady quantum discord (SQD) behavior of a two-qubit anisotropic Heisenberg XYZ chain with different initial states are investigated. We find that properly tuning the external and self parameters not only can improve the quantum correlation and steady quantum correlation but also can weaken the effects of decoherence such as increasing anisotropic parameter Δ, decreasing B or b. When t is infinity, the SQD value and the physical about the SQD phenomenon are studied in detail, the SQD value is strongly dependent on the external and self parameters, which is increased evidently by increasing anisotropic parameter and decreasing nonuniform field. Through analyzing the physical about SQD phenomenon, the conditions about the existence of SQD phenomenon are analyzed with different initial states. These investigations can imply us more control parameters on quantum correlation and steady quantum correlation in solid state systems.

Quantum Discord Behavior for Two Qubits Heisenberg XYZ Chain with Inhomogeneous Magnetic Field

We report the quantum correlation behavior (quantum discord (QD)) of a two-qubit anisotropic Heisenberg XYZ chain under an inhomogeneous magnetic field. It is shown that in the lower region of b QD can be enhanced evidently through increasing anisotropic parameter γ, while the effects of γ are disappear when b is strong enough. The role of J z is nearly opposite to γ, there is a critical value of b c , with b>b c QD is improved with decreasing interaction J z , while the value of QD is nearly invariable whatever changing J z when b<b c . In addition, one can get non-zero QD by properly tuning J z and γ even at a higher temperature. When inhomogeneity is increased to b c , the QD can exhibit a regrowth procession, and the regrowth value of QD can be larger than that of before dropping in the region of weak J z . We also obtain the ground state QD properties. These investigations can imply us more control parameters on quantum correlation in solid state systems.

Dense coding with a two-qubit Heisenberg XYZ chain under the influence of phase decoherence

We investigate the joint effects of phase decoherence, Dzyaloshinskii-Moriya (DM) interaction and inhomogeneity of the external magnetic field (b) on dense coding in a two-qubit anisotropic Heisenberg XYZ spin chain. Analytical expressions are obtained for the dense coding capacity. It is found that valid dense coding is always possible with this model when the system is initially prepared in the maximum entangled state. Moreover, optimal dense coding can be implemented for this initial state as long as the mean spin-spin coupling constant J+ of the XY plane is larger than b and the DM interaction despite the intrinsic decoherence. Non-maximal entangled initial states are found to be undesirable for dense coding with this model.

Thermal entanglement in the XYZ model for a two-qutrit system

The negativity as a measure of thermal entanglement was studied for a two-qutrit spin-1 anisotropic Heisenberg XYZ chain with Dzyaloshinskii–Moriya (DM) interaction in a homogeneous magnetic field in detail. An analytical expression was found for the negativity and then the thermal variations of negativity were investigated in full detail for given values of the DM interaction parameter D z , the external magnetic field B, the measure of the anisotropy on the xy-plane γ = ( J x − J y )/( J x + J y ), a parameter J = ( J x + J y )/2 and the bilinear interaction parameter J z along the z-axis.

Teleportation and thermal entanglement in two-qubit Heisenberg XYZ spin chain with the Dzyaloshinski–Moriya interaction and the inhomogeneous magnetic field

This paper studies the average fidelity of teleportation and thermal entanglement for a two-qubit Heisenberg XYZ chain in the presence of both an inhomogeneous magnetic field and a Dzyaloshinski–Moriya interaction. It shows that for a fixed Dz, the increase of bz will broaden the critical temperature at the cost of decreasing the thermal entanglement. And it can modulate the inhomogeneous magnetic field and the Dzyaloshinski–Moriya interaction for the average fidelity of teleportation to be optimal.