Cluster states [1] form a class of multiparty entangled quantum states with surprising and useful properties. The main interest in these states draws from their role as a universal resource in the one-way quantum computer [2,3]: Given a collection of sufficiently many particles that are prepared in a cluster state, one can realize any ► quantum computation by simply measuring the particles, one by one, in a specific order and basis (see Fig. 1). By the measurements, one exploits ► correlations in quantum mechanics which are rich enough to allow for universal logical processing. Owing to this property, the cluster state has attracted considerable attention in recent foundational studies on the power of quantum computation. It has also become an interesting object from the perspective of multipartite entanglement theory and the study of quantum mechanical ► nonlocality.
Cluster states belong to the larger set of so-called graph states [4], which comprise many of the entangled states known in quantum information theory and foundations. Examples include the Bell or Einstein-Podolsky-Rosen (EPR) states, the Greenberger-Horne-Zeilinger (► GHZ) states, and states that appear in quantum error correction. Graph states have been providing a playground for the study of multipartite ► entanglement, and investigating their role as resources in measurement-based quantum computation has revealed connections to other fields, including quantum many-body physics, graph theory, topological codes, statistical physics, and even mathematical logic. For a recent review of these developments see e.g., [5].
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Briegel, H.J. (2009). Cluster States. In: Greenberger, D., Hentschel, K., Weinert, F. (eds) Compendium of Quantum Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70626-7_30
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