Testing equivalence of pure quantum states and graph states under SLOCC

Details Testing equivalence of pure quantum states and graph states under SLOCC Testing equivalence of pure quantum states and graph states under SLOCC

2009-11-24

arxiv.org/abs/0911.4517v2

Int. J. Quant. Inf. 8 (1-2), 395-410 (2010)

Physics

Quantum Physics

9 pages, to appear in International Journal of Quantum Information; Minor typos corrected, updated references.

Scientific paper

10.1142/S0219749910006368

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.

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