TY - GEN

T1 - Entanglement in graph states and its applications

AU - Hein, M.

AU - Dür, W.

AU - Eisert, J.

AU - Raussendorf, R.

AU - Van Den Nest, M.

AU - Briegel, H. J.

PY - 2006

Y1 - 2006

N2 - Graph states form a rich class of entangled states that exhibit key aspects of multipartite entanglement. At the same time, they can be described by a number of parameters that grows only moderately with the system size. They have a variety of applications in quantum information theory, most prominently as algorithmic resources in the context of the one-way quantum computer, but also in other fields such as quantum error correction and multi-partite quantum communication, as well as in the study of foundational issues such as non-locality and decoherence. In this review, we have given a tutorial introduction into the theory of graph states. We have introduced various equivalent ways how to define graph states, and discussed the basic notions and properties of these states. The focus of this review has been on their entanglement properties. These include aspects of non-locality, bi-partite and multi-partite entanglement and its classification in terms of the Schmidt measure, the distillability properties of mixed entangled states close to a pure graph state, as well as the robustness of their entanglement under decoherence. We have also reviewed some of the known applications of graph states, as well as proposals for their experimental implementation. Some of the latter material, specifically about implementations, should thus be taken as preliminary and reflecting only the current state of research.

AB - Graph states form a rich class of entangled states that exhibit key aspects of multipartite entanglement. At the same time, they can be described by a number of parameters that grows only moderately with the system size. They have a variety of applications in quantum information theory, most prominently as algorithmic resources in the context of the one-way quantum computer, but also in other fields such as quantum error correction and multi-partite quantum communication, as well as in the study of foundational issues such as non-locality and decoherence. In this review, we have given a tutorial introduction into the theory of graph states. We have introduced various equivalent ways how to define graph states, and discussed the basic notions and properties of these states. The focus of this review has been on their entanglement properties. These include aspects of non-locality, bi-partite and multi-partite entanglement and its classification in terms of the Schmidt measure, the distillability properties of mixed entangled states close to a pure graph state, as well as the robustness of their entanglement under decoherence. We have also reviewed some of the known applications of graph states, as well as proposals for their experimental implementation. Some of the latter material, specifically about implementations, should thus be taken as preliminary and reflecting only the current state of research.

UR - http://www.scopus.com/inward/record.url?scp=84861950556&partnerID=8YFLogxK

U2 - 10.3254/978-1-61499-018-5-115

DO - 10.3254/978-1-61499-018-5-115

M3 - Conference contribution

AN - SCOPUS:84861950556

SN - 9781586036607

T3 - Proceedings of the International School of Physics "Enrico Fermi"

SP - 115

EP - 218

BT - Proceedings of the International School of Physics "Enrico Fermi"

A2 - Casati, G.

A2 - Shepelyansky, D. L.

A2 - Zoller, P.

A2 - Benenti, G.

PB - IOS Press

T2 - International School of Physics "Enrico Fermi": Quantum Computers, Algorithms and Chaos

Y2 - 5 July 2005 through 15 July 2005

ER -