Entanglement of Valence-Bond-Solid on an Arbitrary Graph
作者： Ying Xu , Vladimir E Korepin
DOI: 10.1088/1751-8113/41/50/505302
关键词: Connectivity 、 Graph state 、 Eigenvalues and eigenvectors 、 Quantum entanglement 、 Discrete mathematics 、 Adiabatic quantum computation 、 Ground state 、 Cluster state 、 Degenerate energy levels 、 Mathematics
摘要: The Affleck-Kennedy-Lieb-Tasaki (AKLT) spin interacting model can be defined on an arbitrary graph. We explain the construction of AKLT Hamiltonian. Given certain conditions, ground state is unique and known as Valence-Bond-Solid (VBS) state. It used in measurement-based quantum computation a resource instead cluster study VBS connected graph cut into two disconnected parts: block environment. entanglement between these parts prove that many eigenvalues density matrix are zero. describe subspace eigenvectors corresponding to non-zero eigenvalues. degenerate states some Hamiltonian which we call
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128.84.21.199参考文章(94)
B. Nachtergaele, Working with Quantum Markov States and their classical analogues Quantum Probability and Applications V. ,vol. 1442, pp. 267- 285 ,(1990) , 10.1007/BFB0085520
Heng Fan, Vladimir Korepin, Vwani Roychowdhury, Christopher Hadley, Sougato Bose, None, Boundary effects on entropy and two-site entanglement of the spin-1 valence-bond solid Physical Review B. ,vol. 76, pp. 014428- ,(2007) , 10.1103/PHYSREVB.76.014428
Assa Auerbach, Interacting electrons and quantum magnetism ,(1994)
Jeffrey Bub, Quantum information and computation Nature. ,vol. 404, pp. 247- 255 ,(2000) , 10.1038/35005001
Isaac L. Chuang, Michael A. Nielsen, Quantum Computation and Quantum Information ,(2000)
Vwani Roychowdhury, Heng Fan, Vladimir Korepin, Valence-Bond-Solid state entanglement in a 2-D Cayley tree arXiv: Quantum Physics. ,(2005)
Sabre Kais, R. D. Levine, Jiaxiang Wang, F. Remacle, Size effects in the electronic properties of finite arrays of exchange coupled quantum dots: A renormalization group approach arXiv: Quantum Physics. ,(2004)
G. Vidal, J. I. Latorre, E. Rico, Ground state entanglement in quantum spin chains Quantum Information & Computation. ,vol. 4, pp. 48- 92 ,(2004) , 10.5555/2011572.2011576
J. Dreissig, M. Cramer, J. Eisert, M. B. Plenio, Geometric Entropy in Harmonic Lattice Systems ,(2004)
V. E. Korepin, Universality of entropy scaling in one dimensional gapless models. Physical Review Letters. ,vol. 92, pp. 096402- ,(2004) , 10.1103/PHYSREVLETT.92.096402