Entanglement control in one-dimensional $s=12$ random XY spin chain.pdf

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Entanglement control in one-dimensional $s=12$ random XY spin chain.pdf

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Entanglement control in one-dimensional $s=12$ random XY spin chain

a r X i v : 0 8 0 8 .3 6 7 8 v 1 [ q u a n t - p h ] 2 7 A u g 2 0 0 8 Entanglement control in one-dimensional s = 1 2 random XY spin chain ? C. J. Shan ? , W. W. Cheng, T. K. Liu ? , Y. X. Huang, and H. Li College of Physics and Electronic Science, Hubei Normal University, Huangshi 435002, China (Dated: August 27, 2008) Abstract The entanglement in one-dimensional random XY spin systems where the impurities of exchange cou- plings and the external magnetic fields are considered as random variables is investigated by solving the different spin-spin correlation functions and the average magnetization per spin. The entanglement dynam- ics near particular locations of the system is also studied when the exchange couplings (or the external magnetic fields) satisfy three different distributions(the Gaussian distribution, double-Gaussian distribu- tion, and bimodal distribution). We find that the entanglement can be controlled by varying the strength of external magnetic field and the different distributions of impurities. Moreover, the entanglement of some nearest-neighboring qubits can be increased for certain parameter values of the three different distributions. PACS numbers: 03.65.Ud, 03.67.Mn, 75.10.Pq Keywords: the entanglement, spin chain, spin-spin correlation function, Gaussian distribution ? Supported by the Key Higher Education Programme of Hubei Province under Grant No the Natural Science Foundation of Hubei Province, China under Grant No 2006ABA055, and the Postgraduate Programme of Hubei Normal University under Grant No 2007D20. ? E-mail: scj1122@163.com ? Corresponding author. E-mail: tkliuhs@163.com 1 I. INTRODUCTION Entanglement not only has the interesting properties of quantum mechanics but also is very important in the quantum information processing (QIP), such as quantum teleportation [1] , dense coding [2] , quantum secret sharing [3] , quantum computation [4] and some cryptographic protocols [5] . In order to realize the quantum