Multiparticle entanglement purification for two-colorable graph states

Abstract

We investigate multiparticle entanglement purification schemes which allow\none to purify all two colorable graph states, a class of states which includes\ne.g. cluster states, GHZ states and codewords of various error correction\ncodes. The schemes include both recurrence protocols and hashing protocols. We\nanalyze these schemes under realistic conditions and observe for a generic\nerror model that the threshold value for imperfect local operations depends on\nthe structure of the corresponding interaction graph, but is otherwise\nindependent of the number of parties. The qualitative behavior can be\nunderstood from an analytically solvable model which deals only with a\nrestricted class of errors. We compare direct multiparticle entanglement\npurification protocols with schemes based on bipartite entanglement\npurification and show that the direct multiparticle entanglement purification\nis more efficient and the achievable fidelity of the purified states is larger.\nWe also show that the purification protocol allows one to produce private\nentanglement, an important aspect when using the produced entangled states for\nsecure applications. Finally we discuss an experimental realization of a\nmultiparty purification protocol in optical lattices which is issued to improve\nthe fidelity of cluster states created in such systems.\n

Keywords

Affiliated Institutions

• Institute for Quantum Optics and Quantum Information Innsbruck AT
• Ludwig-Maximilians-Universität München DE
• Universität Innsbruck AT

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