Testing equivalence of pure quantum states and graph states under SLOCC

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D'Souza, Adam G.
Briët, Jop
Feder, David L.
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Abstract
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A set of necessary and sufficient conditions are derived for the equivalence of an arbitrary pure state and a graph state on n qubits under stochastic local operations and classical communication (SLOCC), using the stabilizer formalism. Because all stabilizer states are equivalent to a graph state by local unitary transformations, these conditions constitute a classical algorithm for the determination of SLOCC-equivalence of pure states and stabilizer states. This algorithm provides a distinct advantage over the direct solution of the SLOCC-equivalence condition for an unknown invertible local operator S, as it usually allows for easy detection of states that are not SLOCC-equivalent to graph states.
Comment: 9 pages, to appear in International Journal of Quantum Information; Minor typos corrected, updated references.
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Quantum Physics
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