Mediated Entanglement And Correlations In A Star Network Of Interacting   Spins
  We investigate analytically a star network of spins, in which all spins interact exclusively with a central spin through Heisenberg XX couplings of equal strength. We find that the central spin correlates and entangles the other spins at zero temperature to a degree that depends on the total number of spins. Surprisingly, the entanglement depends on the evenness or oddness of this number and some correlations are substantial even for an infinite collection of spins. We show how symmetric multi-party states for optimal sharing and splitting of entanglement can be obtained in this system using a magnetic field. 
A. Hutton, S. Bose