Preparation Of Multi-Qubit Entangled States

Quantum information, based on quantum mechanics, is a subject using quantumtheory of microscopic particles to resolve problems which can not be resolved by clas-sical information and classical computation. It can break through physical limitations ofcurrent information technology to exploit new functions of information. In quantum in-formation processing, storing, denoting and extracting of information are dependent onquantum states and their evolution. Because quantum entanglement is associated with thepeculiar nonclassical correlations, it plays an important role in quantum information pro-cessing and is at the heart of quantum information. Quantum system, in which quantuminformation is prepared, transmitted and stored, often interacts with environment, whichresults the loss of information, and this phenomenon is called decoherence. Therefore,quantum entanglement and quantum coherence are important resources of quantum infor-mation. Thus, the problems about how to prepare entangled state, control the evolutionof quantum state and keep quantum coherence have become the most important subjectof quantum physics. For the preparation of entangled states, the cases of two qubit are in-vestigated extensively. However, multi-qubit entangled states have more advantages thanthe two qubit entangled states in their applications in quantum cloning, teleportation anddense coding, so in this paper, we mainly study the theoretical schemes for preparing afew multi-qubit entangled states by using cavity QED technology, cavity-assisted photonscattering technology and spin network, respectively, and analyze the feasibility of theschemes, then discuss how to eliminate the in?uence of quantum decoherence.Because quantum decoherence can destroy quantum entanglement, improving ourunderstanding on entanglement dynamics and properties is necessary for manipulatingentanglement and resisting the in?uence of decoherence. Therefore, we make a prelim-inary investigation of the entanglement dynamics via Concurrence of two distant atomsinteracting off-resonantly with two cavity fields, respectively, and a comparison betweenConcurrence and Negativity about their evaluation on entanglement. We show that theevolution of entanglement has sudden death and sudden birth phenomena and with theincreasing of photon number in the two cavities, the alternative frequencies of suddendeath and sudden birth get fast and the amplitude of Concurrence oscillates regularly with oscillation frequency becoming slow when the cavity fields have same photon numbers.Whereas, the maximum of Concurrence declines and the amplitude of Concurrence os-cillates irregularly when the two cavity fields have different photon numbers. In addition,we find that the length of death time is dependent on the degree of entanglement of theinitial state.In cavity QED, we propose two scheme for preparing the three-atom W state andthe GHZ state respectively, with oneΛ-type atom and two two-level atoms interactingresonantly with two modes or one mode of a two-mode field in turns. By controlling theevolution time of quantum state appropriately, we can obtain the three-atom W state andthree-atom GHZ state. When we consider the atomic spontaneous emission and cavitydecay, we can obtain high-fidelity entanglement as long as the schemes work beyond thestrong-coupling regime.With cavity-assisted photon scattering technology, we propose a theoretical schemefor generating a newχ-type four-atom entangled state∣χ00?3214 for the first time. In thescheme, we generate successfully theχ-type four-atom entangled states∣χ00?3214 by usingthe controlled phase ?ip gate with atom and single-photon, simple linear optics elements,and a conventional photon detector. Because the photon has weak interaction with theenvironment, it is suitable for distant information transmission, so the state∣χ00?3214 canbe generated with probability 1 as long as there is no photon loss.The decoherence precesses caused by the in?uence of the environment often easilydestroy entanglement and furthermore cause noise in the communication or errors in theoutcomes of computation. In order to overcome decoherence, we may encode logicalqubits into a subspace of the whole Hilbert space, a decoherence-free subspace (DFS),thus the noise and errors can be resisted efficiently. Similarly, by using cavity-assistedphoton scattering technology we propose a scheme for generating arbitrary four-atomentangled DFS states. By conveniently tuning the titled angle of one half-wave plate, wecan obtain arbitrary four-atom entangled DFS states with probability 1 as long as there isno photon loss.Compared with cavity QED and linear optics systems, solid-state qubit can be ex-tended more easily for generating multi-qubit entangled states. Based on spin networks,we propose efficient schemes for preparing multi-qubit graph states. At first, we deriveχSWAP gate for XY interaction, and then we prepare the three classical types of four- qubit graph states inequivalent each other under local unitary transformations and graphisomorphism, and four classical types of five-qubit graph states inequivalent, by usingχSWAP-gate and some single-qubit rotations. By usingχSWAP gate for spin networks,our method makes the generation of multipartite entangled graph states more efficient thanthe ones based on conventional controlled-NOT and controlled phase ?ip gate for solid-state devices, due to its short interaction time and its strong entanglement forχSWAP-gatein solid-state system, so it can overcome the in?uence of quantum decoherence and facil-itates the scalable quantum computation.