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We give a complete structural characterisation of the map the positive branch of a one-way pattern implements. We start with the representation of the positive branch in terms of the phase map decomposition , which is then further analysed to obtain the primary structure of the matrix M, representing the phase map decomposition in the computational basis. Using this approach we obtain some preliminary results on the connection between the columns structure of a given unitary and the angles of measurements in a pattern that implements it. We believe this work is a step forward towards a full characterisation of those unitaries with an efficient one-way model implementation.
|Title of host publication||Proceedings Sixth Workshop on Developments in Computational Models: Causality, Computation, and Physics,|
|Subtitle of host publication||DCM 2010, Edinburgh, Scotland, 9-10th July 2010.|
|Number of pages||16|
|Publication status||Published - 2010|