Researches On Quantum Entanglement And Quantum Algorithm With Cavity QED And Trapped Ions

Quantum entanglement, composed of two-particle entanglement and mult-particleone, is an important resource for quantum information. Compared with two-particleentangled states, mult-particle ones play the more important role in the quantuminformation processing and quantum computation, such as GHZ states, W states andCluster states. Quantum computation is not only a challenge research region, but also theelement motive for studying quantum information. Cluster state, a special mult-particleentangled state and a resource for one-way computer, attracts much public attention eversince it was introduced. Quantum algorithm, acting as processing software for quantumcomputer, can provide paralleling computing which a classical computer can never do.Since the cavity QED and the trapped ions are two very important physical systems bywhich the theories of quantum entanglement and quantum computation can bedemonstrated and tested, they play very important roles in studying quantumentanglement and quantum computation. The main contents are as follows:1. Preparation and application of Cluster state. Two schemes for the preparation ofCluster states based cavity QED technology. In the first protocol, we prepare a clusterstate with n two-level atoms in thermal cavity, so that the system is insensitive to thecavity decay and the thermal field. While in the other one, in order to reduce the atomicspontaneous emission, we prepare one-dimension (1D) and two-dimension (2D)multi-cavity Cluster states and 1D and 2D cluster state with multi-particle A-type atoms.Then a remote controlled not gate is implemented via 4-atom cluster state. After that, wepropose a scheme for preparing cluster states in ion-trapped system.2. Implementation of controlled dense coding via cavity decay. As is well known theatomic levels are suitable as memory and the photon is a candidate for flying qubit.Combining with these advantages, we propose a scheme for the implementation ofcontrolled dense coding via cavity decay. In the scheme, the system is insensitive to thecavity decay and the atomic spontaneous emission and the fidelity can approximate100%. 3. Implement the Deutsch-Jozsa algorithm by Schr(o|¨)dinger cat states in cavity QED.The Deutsch-Jozsa algorithm is a simplest quantum algorithm but it demonstrates theadvantage of paralleling computation of quantum computer. In the paper, we propose ascheme for the implementation of the Deutsch-Jozsa algorithm by Schr(o|¨)dinger cat statesin cavity QED, In the present protocol, the Hadamard transformation isn't required andthe system can reduce the effect of the atomic spontaneous emission.