Testing equivalence of pure quantum states and graph states under SLOCC
Abstract
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.
Keywords
Cite
@article{arxiv.0911.4517,
title = {Testing equivalence of pure quantum states and graph states under SLOCC},
author = {Adam G. D'Souza and Jop Briët and David L. Feder},
journal= {arXiv preprint arXiv:0911.4517},
year = {2010}
}
Comments
9 pages, to appear in International Journal of Quantum Information; Minor typos corrected, updated references.