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 graph states 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 |ψ〉 = S|g〉 for an unknown invertible local operator S, as it usually allows for easy detection of states that are not SLOCC-equivalent to graph states.
Additional Metadata
Keywords Quantum information, graph states, SLOCC
MSC None of the above, but in MSC2010 section 68Qxx (msc 68Q99)
THEME Life Sciences (theme 5), Logistics (theme 3)
Publisher World Scientific
Journal International Journal of Quantum Information
Briët, J, Feder, D.L, & D'Souza, A.G. (2010). Testing Equivalence of Pure Quantum States and Graph States under SLOCC. International Journal of Quantum Information, 8(1-2).