Graphical description of the action of Clifford operators on stabilizer states
Abstract
We introduce a graphical representation of stabilizer states and translate the action of Clifford operators on stabilizer states into graph operations on the corresponding stabilizerstate graphs. Our stabilizer graphs are constructed of solid and hollow nodes, with (undirected) edges between nodes and with loops and signs attached to individual nodes. We find that local Clifford transformations are completely described in terms of local complementation on nodes and along edges, loop complementation, and change of node type or sign. Additionally, we show that a small set of equivalence rules generates all graphs corresponding to a given stabilizer state; we do this by constructing an efficient procedure for testing the equality of any two stabilizer graphs.
 Publication:

Physical Review A
 Pub Date:
 April 2008
 DOI:
 10.1103/PhysRevA.77.042307
 arXiv:
 arXiv:quantph/0703278
 Bibcode:
 2008PhRvA..77d2307E
 Keywords:

 03.67.a;
 Quantum information;
 Quantum Physics
 EPrint:
 14 pages, 8 figures. Version 2 contains significant changes. Submitted to PRA