# A representation of extra-special 2-group, entanglement, and Berry phase of two qubits in Yang-Baxter system

A representation of extra-special 2-group, entanglement, and Berry phase of two qubits in... In this paper we show another representations of extra-special 2-groups. Based on this new representation, we infer a $${\mathbb{M}}$$ matrix which obeys the extra-special 2-groups algebra relations. We also derive a unitary $${\breve{R}(\theta,\varphi)}$$ matrix from the $${\mathbb{M}}$$ using the Yang-Baxterization process. A Hamiltonian for the two qubits is constructed from the unitary $${\breve{R}(\theta,\varphi)}$$ matrix. In this way, we study the Berry phase and entanglement of the two-qubit system. The results also establish relations between topological and holonomic quantum computation. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

# A representation of extra-special 2-group, entanglement, and Berry phase of two qubits in Yang-Baxter system

Quantum Information Processing, Volume 11 (6) – Nov 9, 2011
10 pages

/lp/springer-journals/a-representation-of-extra-special-2-group-entanglement-and-berry-phase-d7CVML030x
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/s11128-011-0329-8
Publisher site
See Article on Publisher Site

### Abstract

In this paper we show another representations of extra-special 2-groups. Based on this new representation, we infer a $${\mathbb{M}}$$ matrix which obeys the extra-special 2-groups algebra relations. We also derive a unitary $${\breve{R}(\theta,\varphi)}$$ matrix from the $${\mathbb{M}}$$ using the Yang-Baxterization process. A Hamiltonian for the two qubits is constructed from the unitary $${\breve{R}(\theta,\varphi)}$$ matrix. In this way, we study the Berry phase and entanglement of the two-qubit system. The results also establish relations between topological and holonomic quantum computation.

### Journal

Quantum Information ProcessingSpringer Journals

Published: Nov 9, 2011

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