The computational power of the W and GHZ states

作     者：D'Hondt, E Panangaden, P 

作者机构：Free Univ Brussels Dept Math B-1050 Brussels Belgium McGill Univ Sch Comp Sci Montreal PQ H3A 2A7 Canada 

出 版 物：《QUANTUM INFORMATION & COMPUTATION》 (Quantum Inf. Comput.)

年 卷 期：2006年第6卷第2期

页      面：173-183页

核心收录：

学科分类：07[理学] 070201[理学-理论物理] 0702[理学-物理学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

主　　题：distributed algorithms leader election quantum computation entangled states W-state GHZ-state 

摘      要：It is well understood that the use of quantum entanglement significantly enhances the computational power of systems. Much of the attention has focused on Bell states and their multipartite generalizations. However, in the multipartite case it is known that there are several inequivalent classes of states, such as those represented by the W-state and the CHZ-state. Our main contribution is a demonstration of the special computational power of these states in the context of paradigmatic problems from classical distributed computing. Concretely, we show that the W-state is the only pure state that can be used to exactly solve the problem of leader election in anonymous quantum networks. Similarly we show that the GHZ-state is the only one that can be used to solve the problem of distributed consensus when no classical post-processing is considered. These results generalize to a family of W- and GHZ-like states. At the heart of the proofs of these impossibility results lie symmetry arguments.