# 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

Quantum Information Processing, Volume 8 (5) – Aug 19, 2009
15 pages

/lp/springer_journal/entanglement-and-berry-phase-in-a-9-9-yang-baxter-system-63LH0efF1H
Publisher
Springer Journals
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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