Algebraic characterisation of one-way patterns

Details Algebraic characterisation of one-way patterns Algebraic characterisation of one-way patterns

2010-06-08

arxiv.org/abs/1006.1431v1

EPTCS 26, 2010, pp. 85-100

Computer Science

Data Structures and Algorithms

Scientific paper

10.4204/EPTCS.26.8

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.

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