Testing Equivalence of Pure Quantum States and Graph States under SLOCC
International Journal of Quantum Information , Volume 8 - Issue 1-2
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.
|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)|
|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).