**Abstract**
Open alternating spin chain with XY-Hamiltonian is the simplest example of inhomogeneous many-body system which allows us to address the different qubits in the chain by the different Larmor frequencies. Recently, the XY-Hamiltonian of an open finite alternating spin chain has been diagonalized [1, 2] on the basis of a generalization of the classical methods [3] for homogeneous chains and we have possibility to investigate entanglement in this system for quantum information processing tasks. In this work, the pairwise entanglement is investigated in the long alternating open spin chains with XY- Hamiltonian versus the temperature, the chain length, the distance of a pair of spins from the chain ends, and the ratio of spin-spin coupling constants [4]. In particular the bound effect on entanglement in the open spin chain is investigated.

We have investigated the dynamics of the pairwise entanglement in MQ (multiple-quantum) NMR experiments and proposed an entanglement witness on the basis of intensity of MQ coherence of the second order in MQ NMR experiments for two-spin clusters [5]. Hence the entanglement can be studied with advanced technique of MQ NMR showing the perspectives to investigate experimentally the pairwise entanglement in the solid-state clusters. The phenomenological theory of spin-lattice relaxation was developed for such systems in MQ NMR experiment.

The adiabatic demagnetization experiment to produce entangled states in 1-D and 2-D spin clusters will be discussed briefly [6].

[1] E. I. Kuznetsova, E. B. Fel'dman, JETP, 102, 882 (2006).

[2] E. B. Fel'dman and M. G. Rudavets, JETP Letters, 81, 47 (2005).

[3] E. H. Lieb, et al., Ann. Phys., 16, 407, (1961).

[4] S. I. Doronin, A. N. Pyrkov, E. B. Fel'dman "Entanglement in Alternating Open Chains of Nuclear Spins s=1/2 with the XY-Hamiltonian", JETP Letters, 85, 519 (2007).

[5] E. B. Fel'dman, A. N. Pyrkov "Evolution of spin entanglement and an entanglement witness in multiple-quantum NMR experiments", JETP Letters, 88, 398 (2008).

[6] S.I. Doronin, E.B. Fel'dman, M.M. Kucherov, A. N. Pyrkov <>, Journal of Physics: Condensed Matter, Vol. 21, 025601 (2009).