for incorporating it in quantum state transfer protocols. On the other hand, since in quantum measurement the state of the system collapses instantaneously it can be used to induce dynamics in the system by changing its state and thus may be used as an alternative approach to attaching scenarios for quantum communication in strongly correlated systems.

Cold atoms in an optical lattice are excellent test bed for many-body experiments. Both bosons [@Mott-insulator-boson] and fermions [@Mott-insulator-fermion] have been realized in the Mott insulator phase, where there is exactly one atom per site, and by properly controlling the intensity of laser beams one can tune the interaction between neutral atoms to behave as an effective spin Hamiltonian [@Lukin]. Local addressability of atoms with the resolution of single sites [@Bloch-single-site1; @Bloch-single-site2] has opened a totally new window for exploring many-body systems. Single site unitary operations and measurements [@Bloch-single-site2; @Meschede; @Bloch-spin-wave; @Bloch-magnon] are in fact becoming viable and accessible with high fidelities. Thanks to these new advancements, the correlated particle-hole pairs and string orders [@Bloch-particle-hole] together with their time evolution [@Bloch-correlation-time] have been explored experimentally. Furthermore, in recent experiments the propagation of a single impurity spin [@Bloch-spin-wave] and magnon bound states [@Bloch-magnon] in a 