Local equivalence of complete bipartite and repeater graph states

Ilan Tzitrin
Phys. Rev. A 98, 032305 – Published 6 September 2018

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.

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  • Received 25 May 2018

DOI:https://doi.org/10.1103/PhysRevA.98.032305

©2018 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & Technology

Authors & Affiliations

Ilan Tzitrin*

  • Department of Physics, University of Toronto, Toronto, Ontario, Canada M5S 1A7

  • *itzitrin@physics.utoronto.ca

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Issue

Vol. 98, Iss. 3 — September 2018

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