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A method to construct all representations of finite dimensional unitary matrices as the product of Householder reflections is given. By arbitrarily severing the state space into orthogonal subspaces, the method may, e.g., identify the entangling and single-component quantum operations that are required in the engineering of quantum states of composite (multi-partite) systems. Earlier constructions are shown to be extreme cases of the unifying scheme that is presented here.

The phenomenon of synchronization in pairs of cellular automata coupled in a driver-replica mode is studied. Necessary and sufficient conditions for synchronization in linear cellular automaton pairs are given. The couplings that make a pair synchronize are determined for all linear elementary cellular automata. (c) 1998 American Institute of Physics.

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The no-signaling approach to nonlocality deals with separable and inseparable multiparty correlations in the same set of probability states without conflicting causality. The set of half-spaces describing the polytope of no-signaling probability states that are admitted by the most general class of Bell scenarios is formulated in full detail. An algorithm for determining the skeleton that solves the no-signaling description is developed upon a new strategy that is partially pivoting and partially incremental. The algorithm is formulated rigorously and its implementation is shown to be effective to deal with the highly degenerate no-signaling descriptions. Several applications of the algorithm as a tool for the study of quantum nonlocality are mentioned. Applied to a large set of bipartite Bell scenarios, we found that the corresponding no-signaling polytopes have a striking high degeneracy that grows up exponentially with the size of the Bell scenario.