Three-qubit Heisenberg Research Articles

Bell-nonlocality sudden birth with intrinsic decoherence

Taking into account the intrinsic decoherence effect, we study the tripartite nonlocality of a three-qubit Heisenberg spin system with three-body interaction by the generalized Bell inequality. We have found that there is Bell-nonlocality sudden birth, and the three-body interaction is vital to achieving it.

Implementation of the Fredkin gate with a three-qubit mixed-spin Heisenberg model

We show that a local unitary (LU) equivalent Fredkin gate can be obtained from the free evolution of three mixed-spin qubits by virtue of numerical simulation with only one step. The spin-1 qubit acts as the control qubit, and two spin-1/2 qubits, which interact with the spin-1 qubit via the first neighbor spin interaction, respectively, play the role of target qubits. We also examine the imperfect Fredkin gate operation by considering the effects of nonidentical coupling constants, uniform and inhomogeneous magnetic fields.

Quantum phase transition and entanglement in Heisenberg XX spin chain with impurity

In this paper, we study the quantum phase transition and the effect of impurity on the thermal entanglement between any two lattices in three-qubit Heisenberg XX chain in a uniform magnetic field. We show that the quantum phase transition always appears when impurity parameter is an arbitrary constant and unequal to zero, the external magnetic field and impurity parameters have a great effect on it. Also, there exists a relation between the quantum phase transition and the entanglement. By modulating the temperature, magnetic field and the impurity parameters, the entanglement between any two lattices can exhibit platform-like behaviour, which can be used to realize entanglement switch.

Tripartite states Bell-nonlocality sudden death with intrinsic decoherence

Taking the intrinsic decoherence effect into account, the tripartite nonlocality is measured by the extent of violation of multipartite Bell inequality in a three-qubit Heisenberg XY chain in the presence of an external magnetic field. It is shown that multipartite Bell-inequality violations can be destroyed in finite time in the system and the influence of the intrinsic decoherence on the tripartite states Bell-nonlocality sudden death is demonstrated.

DYNAMICS OF PAIRWISE ENTANGLEMENT IN THE THREE-QUBIT HEISENBERG XX SPIN CHAIN

For a three-qubit Heisenberg XX spin chain with the uniform magnetic field and magnetic impurity, dynamic evolution of pairwise entanglement are studied. We show that the phenomenon of entanglement sudden death (ESD) occurs in the evolution of entanglement for some initial states. We also find that magnetic impurity cannot only eliminate the phenomenon of ESD but also induce the ESD effects, which is different from the case of uniform magnetic field where the ESD can be depressed but cannot be eliminated by introducing the uniform magnetic field.

Thermal entanglement and teleportation in a three-qubit Heisenberg XXZ model with Dzyaloshinski–Moriya anisotropic antisymmetric interaction

This paper investigates the thermal pairwise entanglement of a three-qubit Heisenberg XXZ chain in the presence of the Dzyaloshinski–Moriya (DM) anisotropic antisymmetric interaction and quantum teleportation when using the Heisenberg chain as a channel. The entanglement dependences on the DM interaction and temperature are given in detail. It obtains the relation between the concurrence and average fidelity, and shows that the same concurrence can lead different average fidelities. Moreover, it finds the thermally entangled states which do not violate the Bell inequalities, and can still be used for quantum teleportation.

Pairwise entanglement of a three-qubit Heisenberg XY chain in a nonuniform magnetic field with intrinsic decoherence

Taking into account the intrinsic decoherence, the concurrence of the nearest and the next-to-nearest neighbor qubits in a three-qubit Heisenberg XY chain are investigated when a nonuniform magnetic field is included. We show that the effects of the external magnetic field, including the uniform and inhomogeneous magnetic fields, on the time evolution of entanglement between the nearest and the next-to-nearest neighbor qubits rely deeply on the initial states. We can moderate the destructive effect of intrinsic decoherence by controlling the uniform and inhomogeneous magnetic fields, so that a proper value of uniform and inhomogeneous magnetic fields can, to a great extent enhance the stationary entanglement.

Pairwise entanglement in three-qubit Heisenberg model with Dzyaloshinskii-Moriya interaction

In this paper, we study the improvement and manipulation of pairwise thermal entanglement in one-dimentional three-qubit Heisenberg model, where Dzyaloshinskii-Moriya （DM） interaction is considered and concurrence is calculated to research this entanglements property. The results show that for XXX model, DM interaction can induce entanglement in the antiferromagnetic and ferromagnetic spin chains although the required critical values are different for these cases. For XXZ model, by introducing DM interaction D, antiferromagnetic spin chain has entanglement which is absent when D=0, and in addition, for antiferromagnetic and ferromagnetic cases, DM interaction D and the anisotropy parameter Δ have different effects on entanglement. As a result, the entanglement can be controlled and enhanced by choosing appropriate DM interaction and anisotropy parameter. Furthermore, we find that at the same temperature, no matter for antiferromagnetic or ferromagnetic spin chains, the critical DM interaction inducing entanglement should be greater in a three-qubit XXZ model than that in a two-qubit XXZ model.

Thermal Entanglement of a Three-Qubit Heisenberg Chain with a Nonuniform Magnetic Field

The thermal entanglement of a three-qubit Heisenberg chain under a nonuniform magnetic field is studied. It is very interesting to note that the next nearest neighbor entanglement (NNNE) could be larger than the nearest neighbor entanglement (NNE). We analyze the ground state entanglement, and give the conditions that NNNE is larger than NNE near zero temperature. Our results also show that the nonuniform field could induce the entanglement and improve the threshold temperature at certain parameter region.

Magnetic impurity effects on quantum teleportation via the three-qubit Heisenberg XX model

We study the quantum teleportation through the three-qubit Heisenberg XX model with a magnetic impurity. The main result is the systematic analysis of the average fidelity's evolution as a function of magnetic impurity B and temperature T. What deserves mentioning here is that the effects of magnetic impurity on the average fidelity obviously behave differently whether the impurity is located on the receiver's site or not.

Effects of impurity on the entanglement of the three-qubit Heisenberg XXX spin chain

We investigate the entanglement of the three-qubit Heisenberg XXX chain in the presence of impurity and obtain the analytical expressions of the concurrence C. It is found that for impurity entanglement, C appears only when J 1 > J for J > 0, and J 1 > 0 for J < 0, and in these two regions C increases with the increase of J 1, so is the critical temperature T c. When J 1 ≫ | J |, C reaches its maximum value 0.5 and T c reaches the asymptotic value T c = 3.41448J 1. For entanglement between the normal lattices, C appears only when J > 0 and −2J < J 1 < J, and initially increases with the increase of J 1 and arrives at the maximum value C max = (e4J/T −3)/(e4J/T + 3) before it decays to zero gradually, so is the critical temperature T c with, however, the maximum value T cmax = 4J/In3.

Control of impurity over entanglement in Heisenberg chain

The thermal entanglement in a three-qubit Heisenberg XXX spin chains with a impurity site is investigated under an external magnetic field. For a fixed ξ ( ξ = 2 or - 2 ) , we discussed the effect of the impurity parameter γ and the magnetic field B to the concurrence. The calculation results reveal that the impurity parameter γ and the magnetic field B can significantly effect the pair entanglement between the spin lattices with a different way on the case of anti-ferromagnetic ( ξ = 2 ) or ferromagnetic ( ξ = - 2 ).

Entanglement in the three-qubit Heisenberg model with next nearest neighbor interaction and a nonuniform magnetic field

Pairwise thermal entanglement in the three-qubit XXX Heisenberg model with next nearest neighbor interaction and a nonuniform magnetic field has been studied. It's found that the next nearest neighbor interaction has a great effect on the entanglement between the next nearest neighbor sites, but has slight effect on the nearest neighbor entanglement (NNE). Applying a magnetic field at the middle site enhances the next nearest neighbor entanglement (NNNE) sharply when there is a small field at the side sites and the next nearest neighbor coupling constant is positive. A staggered magnetic field helps to maintain nearest neighbor entanglement obviously.

Magnetic impurity effects on the entanglement of three-qubit Heisenberg XY chain with intrinsic decoherence

We investigate a three-qubit Heisenberg XY chain with magnetic impurity in the model of Milburn's intrinsic decoherence and the pairwise entanglement is calculated by making use of the concurrence. It is shown that the nearest neighbor pairwise entanglement rapidly decay due to intrinsic decoherence, but next to nearest neighbor qubits finally stay in a entangled stationary state in the case without the magnetic impurity. The magnetic impurity in the central qubit can protect the nearest neighbor pairwise entanglement from being completely destroyed by the intrinsic decoherence.

The effect of impurity on the entanglement between the normal lattice in three-qubit Heisenberg XX chain

In this paper,we study the effect of impurity on the thermal entanglement between the normal lattice in three-qubit Heisenberg XX chain,and give the analytical expression of the concurrence.According to the discussion of our result,we find that the impurity parameter has a great effect on the pairwise thermal entanglement,it even can change the characters of the entanglement to some degree.

Studying the thermally entangled state of a three-qubit HeisenbergXXring via quantum teleportation

We consider quantum teleportation as a tool to investigate the thermally entangled state of a three-qubit Heisenberg $\mathrm{XX}$ ring. Our investigation reveals interesting aspects of quantum entanglement not reflected by the pairwise thermal concurrence of the state. In particular, two mixtures of different pairs of W states, which result in the same concurrence, could yield very different average teleportation fidelities.

Impurity entanglement in three-qubit Heisenberg XX chain

We studied the influence of the impurity to the entanglement in three-qubit Heisenberg XX chain and got the analytical expression of the concurrence C , go a step further, for fixed J, we discussed the concrete effect of the impurity parameter J 1 to the concurrence. At the condition T→0, when | J 1|⪢| J|, the concurrence C=(2 2 −1)/4 ; when J 1→− J and J→∞, the concurrence C get its maximum value 1/2.

Thermal entanglement in three-qubit Heisenberg models

We study pairwise thermal entanglement in three-qubit Heisenberg models and obtain analytic expressions for the concurrence. We find that thermal entanglement is absent from both the antiferromagnetic $XXZ$ model, and the ferromagnetic $XXZ$ model with anisotropy parameter $\Delta\ge 1$. Conditions for the existence of thermal entanglement are discussed in detail, as is the role of degeneracy and the effects of magnetic fields on thermal entanglement and the quantum phase transition. Specifically, we find that the magnetic field can induce entanglement in the antiferromagnetic $XXX$ model, but cannot induce entanglement in the ferromagnetic $XXX$ model.