The Computational Power of the W and GHZ states

Details The Computational Power of the W and GHZ states The Computational Power of the W and GHZ states

2004-12-22

arxiv.org/abs/quant-ph/0412177v2

Journ. Quantum Inf. and Comp., vol. 6(2), pages 173-183, 2005

Physics

Quantum Physics

11 pages, substantial rewrite based on referee reports

Scientific paper

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 GHZ-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.

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