Studies Of Quantum Hypergraph Coding And Entanglement Measure

Quantum computing and quantum information is an information science which is based on quantum mechanics and theoretical computer. Such quantum algorithms have been found, which shows that universal quantum computation has great potential beyond the ordinary deterministic turning computing. Quantum computing has become the forefront filed and direction of one of the most talked about. The understanding of the subtle properties of multipartite entangled states is at the very heart of quantum information theory, but the ultimate goal of coping with the properties of arbitrary multipartite states is far from being reached. Therefore, several special classes of entangled states have been introduced and identified as useful for certain tasks. For instance, cluster states are known to serve as a universal resource for quantum computing in oneway quantum computer. Greenberger-Horne-Zeilinger(GHZ) states and W states occur in quantum communication. Stabilizer states can be employed for quantum error correction to protect quantum states against decoherence in quantum computation.It is important to identify the relationship among different classes of entangled states. Graph states can describe a large family of entangled states including cluster states, GHZ states, and stabilizer states. But graph states cannot represent all entangled states(for instance, W states). Ionicioiu and Spiller have presented an axiomatic framework that is for mapping graphs to quantum states of a suitable physical system. In this way, graphscan be encoded into the quantum state, which are graph states. After this, these frameworks have been extended to the directed graph and weighted chart. Further more, research of the author's supervisor and predecessor promots the state of graph to the state of hypergraphs so that more quantum states can be described.Kruszynska and Kraus have recently introduced the so-called locally maximally entangleable(LME) states of n qubits which can be maximally entangled with local auxiliary qubits using controlled operations. Based on the above recognitions, we analyzed the relationship among LME, W states and hypergraph tates under local unitary transformations. Moreover, we also present an approach for encoding weighted hypergraphs into LME states. And we introduce an approach for computing local entropic measure on qubit t of a hypergraph state by using the Hamming weight of the so-called t-adjacent subhypergraph. Then, we quantify and characterize the entanglement of hypergraph states in terms of local entropic measures obtained by using the above approach. Our results show the relationship between full-rank hypergraph states of more than two qubits and graph state under local unitary transformations.