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Investigation of thermal entanglement in quantum information theory

Bahram Bahmani, G. Najarbashi, Leila Balazadeh

Published Jan 1, 2016• 0 citations
OpenAlex

Abstract

Thermal entanglement of spins are investigated in the several Heisenberg models by using of various entanglement measures, and we will evaluate the quantity of thermal entanglement with different parameters of the system (such as, magnetic field, temperture, impurity and different components of interaction). In part of proceduring, we will show that entanglement between two spins have a gaussian profile at the low temperature, and we show that there exists a relation between the QPT and the entanglement in three – qubit Heisenberg chain under the effect of impurity. In fact, QPT is the structure change in property of the ground state at the many–body system, which occures at absolute zero temperature and is purely driven by quantum fluctuation. This transitions appear with the change of a physical parameter. Thus we expect that phase transitions and critical behavior of systems can be explained by entanglement. Also, we investigate the entanglement in pure and thermal cluster states and pay attention to entanglement generation from thermal spin states inputed in a beam spliter. Then, thermal entanglement of Bosonic atoms are investigated in an optical lattices with nonlinear couplings and inhomogeneous magnetic field parameters by using of Negativity measure. We understand from the receiving results that nonlinear coupling coefficient support to entanglement can be improve under antiparalel magnetic field. Finally, we investigate quantum Teleportation at the Heisenberg model in presence of system impurity, as the result of quantum entanglement. We will demonstrate that the Fidelity average, as the measure for evaluation quantum Teleportation, can be controled by modulating magnetic field and impurity parameter Keywords: Beam Spliter, Closest Separable State, Concurrence, Entanglement, Fidelity Average, Generation Entanglement, Ground State Entanglement, Heisenberg Model, Impurity, Inhomogenous, Negativity, Nonlinear Coupling, Normal Lattice, Pure Cluster States, Pure state, Quantum Phase Transition, Quantum Teleportation, Thermal Entanglement.

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In this paper, the features of quantum teleportation of a maximally entangled input thermal state using a system, consisting of two qubits (spin-1/2) anisotropic XY Heisenberg model with Herring–Flicker coupling in the presence of a magnetic field, are discussed. So, we study the influence on the thermal entanglement of different physical parameters such as temperature [Formula: see text], magnetic field [Formula: see text], degree of anisotropy [Formula: see text] and distance [Formula: see text] between the two spins. The goal is to determine the conditions of use of the system as a good channel to promote quantum teleportation. The amount of output entanglement is quantified by the concurrence [Formula: see text], and the quality of teleportation is analyzed using the concept of fidelity [Formula: see text]. It is shown that [Formula: see text] presents a maximum at extremely low temperature for a large range of the parameter [Formula: see text]. Also, when we increase the temperature, we observe a dissipation of the appropriate range of [Formula: see text] and the decrease of the amplitude of [Formula: see text]. Besides, under an external magnetic field [Formula: see text], we show the appearance of quantum phase transitions with the entanglement vanishing when the condition [Formula: see text] is fulfilled, then the system can ensure the ideal communication transmission. Concerning the Ising model [Formula: see text] in the ground state, the output entanglement is nonzero only in the presence of the magnetic field [Formula: see text], and this model is useful for ensuring a distorted transmission. At finite temperature, the fidelity [Formula: see text] is less than the value 2/3, so that the system is useless as a quantum channel for providing quantum teleportation.

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Acta Physica Sinica•Jan 1, 2018•0 citations
Thermal entanglement of spins are investigated in the several Heisenberg models by using of various entanglement measures, and we will evaluate the quantity of thermal entanglement with different parameters of the system (such as, magnetic field, temperture, impurity and different components of interaction). In part of proceduring, we will show that entanglement between two spins have a gaussian profile at the low temperature, and we show that there exists a relation between the QPT and the entanglement in three – qubit Heisenberg chain under the effect of impurity. In fact, QPT is the structure change in property of the ground state at the many–body system, which occures at absolute zero temperature and is purely driven by quantum fluctuation. This transitions appear with the change of a physical parameter. Thus we expect that phase transitions and critical behavior of systems can be explained by entanglement. Also, we investigate the entanglement in pure and thermal cluster states and pay attention to entanglement generation from thermal spin states inputed in a beam spliter. Then, thermal entanglement of Bosonic atoms are investigated in an optical lattices with nonlinear couplings and inhomogeneous magnetic field parameters by using of Negativity measure. We understand from the receiving results that nonlinear coupling coefficient support to entanglement can be improve under antiparalel magnetic field. Finally, we investigate quantum Teleportation at the Heisenberg model in presence of system impurity, as the result of quantum entanglement. We will demonstrate that the Fidelity average, as the measure for evaluation quantum Teleportation, can be controled by modulating magnetic field and impurity parameter
Keywords:
Beam Spliter, Closest Separable State, Concurrence, Entanglement, Fidelity Average, Generation Entanglement, Ground State Entanglement, Heisenberg Model, Impurity, Inhomogenous, Negativity, Nonlinear Coupling, Normal Lattice, Pure Cluster States, Pure state, Quantum Phase Transition, Quantum Teleportation, Thermal Entanglement.
In this paper, the features of quantum teleportation of a maximally entangled input thermal state using a system, consisting of two qubits (spin-1/2) anisotropic XY Heisenberg model with Herring–Flicker coupling in the presence of a magnetic field, are discussed. So, we study the influence on the thermal entanglement of different physical parameters such as temperature [Formula: see text], magnetic field [Formula: see text], degree of anisotropy [Formula: see text] and distance [Formula: see text] between the two spins. The goal is to determine the conditions of use of the system as a good channel to promote quantum teleportation. The amount of output entanglement is quantified by the concurrence [Formula: see text], and the quality of teleportation is analyzed using the concept of fidelity [Formula: see text]. It is shown that [Formula: see text] presents a maximum at extremely low temperature for a large range of the parameter [Formula: see text]. Also, when we increase the temperature, we observe a dissipation of the appropriate range of [Formula: see text] and the decrease of the amplitude of [Formula: see text]. Besides, under an external magnetic field [Formula: see text], we show the appearance of quantum phase transitions with the entanglement vanishing when the condition [Formula: see text] is fulfilled, then the system can ensure the ideal communication transmission. Concerning the Ising model [Formula: see text] in the ground state, the output entanglement is nonzero only in the presence of the magnetic field [Formula: see text], and this model is useful for ensuring a distorted transmission. At finite temperature, the fidelity [Formula: see text] is less than the value 2/3, so that the system is useless as a quantum channel for providing quantum teleportation.
In this paper, thermal entanglement in four and five-qubit spin-star networks evolved by an XXX Hamiltonian model is studied. We examine the effect of temperature, magnetic field and coupling constant on the concurrence. We will show that the entanglement is decreased by increasing the temperature and the number of qubits. Also, we investigate quantum teleportation via a couple of spin-star networks in a thermal state. The average of fidelity as a function of temperature, magnetic field, and coupling constant is analyzed, too. It will be observed that as the temperature increases, the fidelity first decreases and then tends to a constant value. Moreover, with the increase of the external magnetic field, the average fidelity first increases and then gradually decreases, and in a certain amount of magnetic field, the average fidelity becomes zero. In addition, as the number of qubits increases, fidelity decreases with temperature. The results indicate that mean fidelity increases with increasing coupling constant.
We elucidate the finite temperature entanglement properties of N=9N=9N=9 qubits Heisenberg XXXXXX and XXZXXZXXZ models under the presence of a polarized magnetic field in xzxzxz plane by means of concurrence concept. We perform a systematic analysis for a wide range of the system parameters. Our results suggest that the global phase regions which separate the entangled and non-entangled regions sensitively depend upon the spin-spin interaction term of the z−z-z− component of two neighboring spins Jz/JxJ_{z}/J_{x}Jz​/Jx​, temperature as well as polarized magnetic field components. Thereby, we think that polarized magnetic field can be used a control parameter to determine the amount of thermal entanglement between pair of qubits for different temperatures and spin-spin interaction terms. Moreover, it has been found that the nearest-neighbor pair of qubits does not point out a re-entrant type entanglement character when one only deals with the nearest-neighbor pair of qubits. However, as one considers next-nearest neighbor pair of qubits, it is possible to see the evidences of re-entrant type entanglement behaviors.
The thermal entanglement in a two-qubit anisotropic Heisenberg XXZ system, also XYZ system, with Dzyaloshinskii-Moriya (DM) couplings in an inhomogenous magnetic field, was studied. The effects of these two kinds of anisotropies on the thermal entanglement have been studied in detail in the concept for concurrence, the measure of entanglement. The analytical expressions of concurrence are obtained for this model. It is found that the DM interaction can enhance thermal entanglement and can be efficiently controlled by the DM interaction parameter and ehchange interaction Jx, Jy and Jz. When D is large enough, the entanglement can exist for larger temperatures and strong magnetic field. We also analysed thermodynamic properties of Heisenberg model and the most important results were shown in the paper.
In the study of thermal entanglement of the Heisenberg spin chain model, one usually considers only the spin interaction between the nearest neighboring qubits. Actually, a generalized Heisenberg model, so-called J1-J2 Heisenberg model, which is constructed by considering the fact that not only the nearest neighboring but also the next nearest neighboring spin interaction also plays an important role. In J1-J2 Heisenberg model, due to the next nearest neighboring spin interaction, the frustration effect can occur and has an important influence on the magnetic properties of the model. In this paper we investigate the thermal entanglement of a five-qubit XXZ Heisenberg spin chain with the next nearest neighboring interaction in a magnetic field. Using the numerical method, we calculate the pairwise concurrences of the nearest neighbouring qubits and the next nearest neighboring qubits, abbreviated as C12 and C13 respectively. The numerical results show that the frustration parameter α has an important effect on the pairwise thermal entanglement. Moreover, C12 and C13 have different variations with the change of the frustration parameter α. Meanwhile, it is found that the temperature, magnetic field, Dzyaloshinkii-Moriya (DM) interaction and anisotropic parameter also have great effects on the thermal entanglement. The increasing of temperature can reduce the thermal entanglement. The magnetic field can enhance the thermal entanglement between both two nearest and next nearest neighboring qubits, but when the magnetic field becomes strong enough, only the thermal entanglement between the two nearest neighboring qubits is suppressed. A certain extent of DM interaction can enhance the thermal entanglement between the two nearest neighboring qubits. But for the next nearest neighboring qubits, without the magnetic field, the increasing of DM interaction mainly enlarge the entanglement vanishing area of frustration parameter α. When the system changes from anisotropic to isotropic state, the entanglement vanishing area also changes obviously for C12 and C13. Thus, we can choose appropriate magnetic field strength, temperature, frustration parameter, DM interaction parameter and anisotropic parameter to effectively control and enhance the thermal entanglement of the system.