Entanglement and Berry phase in a 9× 9 Yang–Baxter system

Entanglement and Berry phase in a 9× 9 Yang–Baxter system A M-matrix which satisfies the Hecke algebraic relations is presented. Via the Yang–Baxterization approach, we obtain a unitary solution $${\breve{R}(\theta,\varphi_{1},\varphi_{2})}$$ of Yang–Baxter equation. It is shown that any pure two-qutrit entangled states can be generated via the universal $${\breve{R}}$$ -matrix assisted by local unitary transformations. A Hamiltonian is constructed from the $${\breve{R}}$$ -matrix, and Berry phase of the Yang–Baxter system is investigated. Specifically, for $${\varphi_{1}\,{=}\,\varphi_{2}}$$ , the Hamiltonian can be represented based on three sets of SU(2) operators, and three oscillator Hamiltonians can be obtained. Under this framework, the Berry phase can be interpreted. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

Entanglement and Berry phase in a 9× 9 Yang–Baxter system

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Publisher
Springer US
Copyright
Copyright © 2009 by Springer Science+Business Media, LLC
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-009-0118-9
Publisher site
See Article on Publisher Site

Abstract

A M-matrix which satisfies the Hecke algebraic relations is presented. Via the Yang–Baxterization approach, we obtain a unitary solution $${\breve{R}(\theta,\varphi_{1},\varphi_{2})}$$ of Yang–Baxter equation. It is shown that any pure two-qutrit entangled states can be generated via the universal $${\breve{R}}$$ -matrix assisted by local unitary transformations. A Hamiltonian is constructed from the $${\breve{R}}$$ -matrix, and Berry phase of the Yang–Baxter system is investigated. Specifically, for $${\varphi_{1}\,{=}\,\varphi_{2}}$$ , the Hamiltonian can be represented based on three sets of SU(2) operators, and three oscillator Hamiltonians can be obtained. Under this framework, the Berry phase can be interpreted.

Journal

Quantum Information ProcessingSpringer Journals

Published: Aug 19, 2009

References

  • Geometric phases for mixed states in interferometry
    Sjövist, E.; Pati, A.K.; Ekert, A.; Anandan, J.S.; Ericsson, M.; Oi, D.K.L.; Vedral, V.
  • Deviation from Berry’s adiabatic geometric phase in a 131Xe nuclear gyroscope
    Appelt, S.; Mehring, M.
  • Entanglement of formation of an arbitrary state of two qubits
    Wootters, W.K.
  • Geometric quantum computation
    Ekert, A.; Ericsson, M.; Hayden, P.; Inamori, H.; Jones, J.A.; Oi, D.K.L.; Vedral, V.
  • Some Exact results for the many-body problem in one dimension with repulsive delta–function interaction
    Yang, C.N.

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