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References (25)
-
F Wilczek (1982)
Magnetic flux, angular momentum, and statisticsPhys. Rev. Lett., 48
-
H Xu, X Wan (2008)
Constructing functional braids for low-leakage topological quantum computingPhys. Rev. A, 78
-
AL Owczarek, RJ Baxter (1987)
A class of interaction-round-a-face models and its equivalence with an ice-type modelJ. Stat. Phys., 49
-
V Pasquier (1987)
Two-dimensional critical systems labelled by Dynkin diagramsNucl. Phys. B, 285
-
M Wadati, T Deguchi, Y Akutsu (1989)
Exactly solvable models and knot theoryPhys. Rep., 180
-
H Barnum, E Knill, G Ortiz, L Viola (2003)
Generalizations of entanglement based on coherent states and convex setsPhys. Rev. A, 68
-
LH Kauffman, SJ Lomonaco (2004)
Braiding operators are universal quantum gatesNew J. Phys., 6
-
V Pasquier (1987)
Latttice derivation of modular invariant partition functions on the torusJ. Phys. A, 20
-
PP Kulish (2003)
On spin systems related to the Temperley–Lieb algebraJ. Phys. A Math. Gen., 36
-
C.F. Sun, K. Xue, G.C. Wang, C.C. Zhou, G.J. Du (2011)
The topological basis realization and the corresponding XXX spin chainEPL-Europhys. Lett., 94
-
G Moore, N Read (1991)
Nonabelions in the fractional quantum Hall effectNucl. Phys. B, 360
-
S-W Hu, K Xue, M-L Ge (2008)
Optical simulation of the Yang–Baxter equationPhys. Rev. A, 78
-
A Feiguin, S Trebst, AWW Ludwig, M Troyer, A Kitaev, ZH Wang, MH Freedman (2007)
Interacting anyons in topological quantum liquids: the golden chainPhys. Rev. Lett., 98
-
V Pasquier (1987)
Operator content of the ADE lattice modelsJ. Phys. A, 20
-
R Marx, A Fahmy, L Kauffman, S Lomonaco, A Spörl, N Pomplun, T Schulte-Herbrüggen, JM Myers, SJ Glaser (2009)
Nuclear-magnetic-resonance quantum calculations of the Jones polynomialPhys. Rev. A, 81
-
H. Temperley, E.H. Lieb (1971)
Relations between the percolation and colouring problem and other graphtheoretical problems associated with regular planar lattices: some exact results for the percolation problemProc. R. Soc. (Lond) A, 322
-
C Nayak, SH Simon, A Stern, M Freedman, SD Sarma (2008)
Non-Abelian anyons and topological quantum computationRev. Mod. Phys., 80
-
DA Meyer, NR Wallach (2002)
Global entanglement in multiparticle systemsJ. Math. Phys., 43
-
A Klümper (1989)
New results for q-state vertex models and the pure biquadratic spin-1 HamiltonianEurophys. Lett., 9
-
K Niu, K Xue, Q Zhao, ML Ge (2011)
The role of the $l_{1}$-norm in quantum information theory and two types of the Yang–Baxter equationJ. Phys. A, 44
-
LH Kauffman (1991)
Knots and Physics -
JL Chen, K Xue, ML Ge (2008)
Berry phase and quantum criticality in Yang–Baxter systemsAnn. Phys., 323
-
Y Zhang (2006)
Teleportation, braid group and Temperley–Lieb algebraJ. Phys. A Math. Gen., 39
-
E Ardonne, K Schoutens (2007)
Wavefunctions for topological quantum registersAnn. Phys., 322
-
K Hikami (2008)
Skein theory and topological quantum registers: braiding matrices and topological entanglement entropy of non-Abelian quantum hall statesAnn. Phys., 323
- Publisher
- Springer Journals
- Copyright
- Copyright © 2013 by Springer Science+Business Media New York
- Subject
- Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
- ISSN
- 1570-0755
- eISSN
- 1573-1332
- DOI
- 10.1007/s11128-013-0542-8
- Publisher site
- See Article on Publisher Site
Abstract
In this paper, based on the usual spin basis, we present a complete orthonormal basis with the single loop $$d=\sqrt{2}$$ consisting of maximally entangled four-qubit states. Then we investigate the particular physical properties of the topological basis states in the corresponding quantum spin chains of Temperley–Lieb type. Whether the system is the anti-ferromagnetic case or the ferromagnetic case, the ground states are all doubly degenerate, and they all fall on the topological basis states. Furthermore, we introduce the Yangian $$Y(sl(2))$$ operators to investigate the transitions between the quantum states.
Journal
Quantum Information Processing – Springer Journals
Published: May 12, 2013