Abstract
The phase space for a system of n qubits is a discrete grid of 2n × 2n points, whose axes are labeled in terms of the elements of the finite field to endow it with proper geometrical properties. We analyze the representation of graph states in that phase space, showing that these states can be identified with a class of nonsingular curves. We provide an algebraic representation of the most relevant quantum operations acting on these states and discuss the advantages of this approach.
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