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arXiv · 1007.1751

Graph states in phase space

A. B. Klimov·C. Munoz·L. L. Sanchez-Soto
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Abstract

The phase space for a system of $n$ qubits is a discrete grid of $2^{n} \times 2^{n}$ points, whose axes are labeled in terms of the elements of the finite field $\Gal{2^n}$ 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 non-singular 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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A. B. Klimov, C. Munoz, L. L. Sanchez-Soto. 2010-07-11. Graph states in phase space. https://doi.org/10.1088/1751-8113/45/21/215303

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