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Decomposition of any N-partite state (density operator) into clusters (thatdo not overlap) is studied in detail with a view to learn as much as possibleabout the correlations implied by the state. The Wootters-Mermin theorem,stating that the totality of all strings of cluster events (projectors)determines the state in any finite- or infinite-dimensional state space, is aslightly sharpened and generalized form of the original results of Wootters andMermin. It is applied to tensor factorization of the state into states ofclusters (uncorrelated decomposition) and it is shown that a finestuncorrelated decomposition always exists, and that its coarsenings and onlythey are other possible uncorrelated cluster decompositions. Distant effectswitin homogeneous cluster states, which are, by definition, the tensor factorsin the finest uncorrelated decomposition, are discussed. The entire study isviewed by the author as a possible further elaboration of Mermin's Ithacaprogram.

Quantum Correlations in Multipartite States. Study Based on the Wootters-Mermin Theorem