On the local equivalence of complete bipartite and repeater graph states
arXiv:1805.05968 · doi:10.1103/PhysRevA.98.032305
Abstract
Classifying locally equivalent graph states, and stabilizer states more broadly, is a significant problem in the theories of quantum information and multipartite entanglement. A special focus is given to those graph states for which equivalence through local unitaries implies equivalence through local Clifford unitaries (LU LC). Identification of locally equivalent states in this class is facilitated by a convenient transformation rule on the underlying graphs and an efficient algorithm. Here we investigate the question of local equivalence of the graph states behind the all-photonic quantum repeater. We show that complete bipartite graph (biclique) states, imperfect repeater graph states and small "crazy graph" states satisfy LU LC. We continue by discussing biclique states more generally and placing them in the context of counterexamples to the LU-LC Conjecture. To this end, we offer some alternative proofs and clarifications on existing results.
arXiv comment9 pages, 8 figures
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