Swap Of Quantum Information At The Ends Of An Open Heisenberg Spin Chain

Recently, the investigations of quantum information and quantum computation have attracted much attention in the fields of physics, mathematics and computer science. Quantum algorithm is known for the advantages of high speed and parallel computation. It can be used to deal with some problems which could not be solved efficiently by classical computers. Transferring quantum information can be realized either by the state dynamics of the system or by teleportation utilizing entanglement. The swap action of probability distribution and entanglement at the ends of an open Heisenberg spin chain is discussed in this thesis. The effects of parameters such as magnetic field and coupling strength are analyzed.Firstly, a scheme of realizing the bidirectional transfer of probability information is proposed. The information is encoded in the probability distributions of the states at two end spins. The relative entropy is used to evaluate the effective transmission of the probability. The evolution of the relative entropy shows a periodical behavior. The period is increased with increasing the length of the chain and the magnetic field while it decreases with increasing the coupling strength.Secondly, a scheme of bidirectionally transferring quantum entanglement in an open Heisenberg ferromagnetic spin chain is proposed. The entanglement at the two ends of spin chains can be swapped periodically by applying static magnetic field to the information channel. After a swap period, the entanglement between an uncoupled qubit and one end spin will be shared by the qubit and the other end spin. The relation between the swap action and chain length, magnetic field, couple strength, anisotropic constant is analyzed. Similar swap phenomenon in a four-spin system is discussed analytically.