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Chinese Journal of Quantum Electronics

Thermal entanglement,mixture and quantum communication in a spin chain

Wang Cheng-Zhi

Published Jan 1, 2010• 0 citations
OpenAlex

Abstract

The two-body thermal entanglement and mixture in a three-spin spin chain in thermal equilibrium state are investigated, and the effects of the temperature and magnetic field on the entanglement and mixture are discussed. It is found that, in the ground state, an important class of states, i.e., maximally entangled mixed states, can be generated by controlling magnetic field, which provide a new way to generate maximally entangled mixed states and control entanglement. Further, the spin chain in the thermal equilibrium is used as a quantum channel for quantum communication. The effects of temperature and magnetic field on fidelity are discussed. It is shown that the temperature and magnetic field have vast effects on the fidelity. The relation between fidelity and two-body thermal entanglement is given, which shows that more amount of entanglement does not means higher fidelity.

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The two-body thermal entanglement and mixture in a three-spin spin chain in thermal equilibrium state are investigated, and the effects of the temperature and magnetic field on the entanglement and mixture are discussed. It is found that, in the ground state, an important class of states, i.e., maximally entangled mixed states, can be generated by controlling magnetic field, which provide a new way to generate maximally entangled mixed states and control entanglement. Further, the spin chain in the thermal equilibrium is used as a quantum channel for quantum communication. The effects of temperature and magnetic field on fidelity are discussed. It is shown that the temperature and magnetic field have vast effects on the fidelity. The relation between fidelity and two-body thermal entanglement is given, which shows that more amount of entanglement does not means higher fidelity.
We study the pairwise entanglement and mixture of a three-qubit XXZ spin chain in the ground state in the presence of an external magnetic field B . The effects of the magnetic field, the anisotropy and the temperature on the entanglement and mixture are considered, and entanglement versus the mixture of all the two-spin states is investigated. We find that the maximal entangled mixed state can be obtained in the considered system by controlling the magnetic field. Our results provide another way to generate maximally entangled mixed states.
In the experiment of quantum communication,maximal entangled pure states are difficult to got due to the effects of environment.Therefore,a quantum channel is always represented by a form of mixed states.The thermal equilibrium state in solid state materials is one essential mixed entangled state.In this dissertation,a two-particle entangled state can be teleported through the channel of thermal mixed states in two independent 1D Heisenberg chains.We study the effects of the non-uniform external magnetic field B and temperature T on the entanglement and fidelity.In order to characterize the quality of the teleported state,we make a research of the average fidelity FA.And when B1 and B2 have different directions,the entanglement teleportation is better than the classical teleportation under low temperature.At that case the average fidelity is always larger than 2/3 which is the limited value of the classical teleportation.
This study investigates thermal entanglement in a four-qubit spin chain of Heisenberg model XX with the presence of the Dzyaloshinski-Moriya (DM) anisotropic asymmetric interaction, an external magnetic field, and another parameter. Then, the spin chain was used as a quantum channel for transferring an unknown quantum state. Finally, fidelity concept was used to check the similarity between input state and output state which, in fact, shows the degree of success in teleportation. In this way, the effect of different parameters on the fidelity was determined. It was concluded that quantum channel comprised of four-qubit spin chain which has thermal equilibrium is an appropriate candidate for quantum transfer of information.
The quantum entanglement of the ground state and the thermal entanglement of the mixed thermal state of a three-qubit system with the Heisenberg interaction are investigated in detail in the presence of an inhomogeneous magnetic field. The concurrence of the model is compared with the magnetization, and the threshold temperature of the entanglement is discussed. The effects of the magnetic field and the coupling coefficient in the thermal entanglement are also examined by considering the concurrence of the three-qubit and two-qubit systems. We found that the thermal entanglement of the system exists at temperatures below the threshold temperature even if the ground state is unentangled.
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 we study the entanglement in a two-qubit spin in the XYZ model, and teleport a two-qubit entangled state using this spin chain in the condition of the thermal equilibrium as a quantum channel. We investigate the effects of the interaction of z-component JZ, the inhomogeneous magnetic field b, the anisotropy ?, and the temperature T on the entanglement and fidelity. In order to characterize the quality of the teleported state, we research the average fidelity Fa. High average fidelity of the teleportation is obtained when the temperat ure is very low. Under some condition, we also find that when inhomogeneity increases to a certain value, the average fidelity can exhibit a larger revival than that for less values of b.