Calculating the ground state entanglement of a two-dimensional spin star lattice

Document Type : Full length research Paper

Abstract

In this study, the ground states of a 6-qubit star lattice are studied in the presence of a magnetic field. In addition, their bipartite and multipartite entanglements are obtained, using concurrence as a measure of bipartite entanglement and Meyer–Wallach measure and its generalizations as the measures of multipartite entanglement. Also a comprehensive structure of their entanglement is presented and described. It is shown that the external magnetic field is a tuning agent that determines the separable ground states, the global entangled states and the states between them. Determination of these states helps to choose the required ones, for different quantum information processes.

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[1] K.M. O’Conner, W.K. Wootters, Entangled rings, Physical Review A 63 (2001) 052302-1–052302-9.
[2] X. Wang, Entanglement in the quantum Heisenberg XY model, Physical Review A 64 (2001) 1-7.
[3] D. Gunlycke, S. Bose, V.M. Kendon, V. Vedral, Thermal concurrence mixing in a one-dimensional Ising model, Physical Review A 64 (2001) 1-7.
[4] G.L. Kamta, A.F. Starace, Anisotropy and magnetic field effects on the entanglement of a two qubit Heisenberg XY chain, Physical Review Letters 88 (2002) 1-4.
[5] M. Jafarpour, S. Ghanavati, D. Afshar, Entanglement distribution in a two-dimensional 5-site frustrated J1-J2 spin system: Separable and globally entangled ground states, International Journal of Quantum Information 13 (2015) 1-11.
[6] D.A. Meyer, N.R. Wallach, Global entanglement in multiparticle systems, Journal of Mathematical Physics 43 (2002) 4273-4278.   
[7] G.K. Brennen, An Observable measure of entanglement for pure states of multi-qubit systems, Quantum Information & Computation 3 6(2003) 619-626.
[8] A.J. Scott, Multipartite entanglement quantum-error-correcting codes and entangling power of quantum evolutions, Physical Review A 69 (2004) 1-13.
[9] D.r Bruß, N. Datta, A. Ekert, L. Ch. Kwek, Ch. Macchiavello, Multipartite entanglement in quantum spin chain,  Physical Review A 72 (2005) 1-4.
 [10] R. Jie, ZHU. Shi-Qun, Multipartite Entanglement in Heisenberg Model, Communications in Theoretical Physics 49 (2008) 1449–1452.
[11] T. Roscilde, P. Verrucchi, A. Fubini, S. Haas, V. Tognetti, Entanglement and factorized ground states in two-dimensional quantum antiferromagnets, Physical Review Letters 94 (2005) 1-4.
[12] R.Eryigit, R.Eryigit, Y.Gunduc, Analytical study of thermal entanglement in a two-dimensional J1–J2 model, Physical Letters A 358 (2006)363–367.
[13] R. Zhang, Sh. Zhu, Thermal entanglement in a two-dimensional Heisenberg XY model, Physical Letters A 348 (2006) 110–118.
[14] Q. Xu, S. Kais, M. Naumov, A. Sameh, Exact calculation of entanglement in a 19-site 2D spin system, Physical Review A 81(2010) 1-11.
[15] Q. Xu, G. Sadiek, S. Kais, Dynamics of entanglement in a two-dimensional spin system, Physical Review A 83(2011) 062312-062338.
[16] G. Sadiek, Impurity effect on entanglement in an XY two-dimensional spin lattice, Journal of King Saud University – Science 24 (2012) 331–338.
[17] Q. Xu, G. Sadiek, S. Kais, Tuning entanglement and ergodicity in two-dimensional spin systems using impurities and anisotropy, Physical Review A 85(2012) 1-21.
[18] G. Sadiek, S. Kais, Persistence of entanglement in thermal states of spin systems, Journal of Physics B: Atomic, Molecular and Optical Physics 46(2013) 1-25.
[19] J.I. Cirac, P. Zoller, A scalable quantum computer with ions in an array of microtraps, Nature 404 (2000) 579-581.
[20] S.B. Zheng, G.C. Guo, Efficient scheme for two-atom entanglement and quantum information processing in cavity QED, Physical Review Letters 85(2000) 2392-2395.
 [21] A. Hutton, S. Bose, Comparison of star and ring topologies for entanglement Distribution, Physical Review A 66(2002) 1-14.
[22] A. Hutton, S. Bose, Mediated entanglement  and correlations in a star network of interacting spins, Physical Review A 69 (2004) 1-4.
[23] W.K. Wootters, Entanglement of Formation of an Arbitrary State of Two Qubits, Physical Review Letters 80 (1998) 2245-2248.
[24] P.J. Love et al, A characterization of global entanglement, Quantum Information Processing 6 (2007) 187-195.
[25] U. Scholl Wock, J. Richter, D.J.J. Farnell, R.F. Bishop (Eds.), Quantum Magnetism, Lect. Notes Phys. 645, Springer, Berlin Heidelberg (2004).
[26] Gu. Shi-Jian, Lin. Hai-Qing, Scaling dimension of fidelity susceptibility in quantum phase transitions, Euro physics Letters 87(2009)10003-10005.