chains. The simplicity of the protocol, with all its ingredients available in optical lattice experiments, allows for the experimentation of the proof of principles for measurement induced dynamics along an anti-ferromagnetic chain. Our protocol can also be interpreted as remote state preparation [@Bennet-remote] since a known quantum state is prepared on one side of the chain and then is transferred to the other side which might be inaccessible for some practical issues. In addition, our measurement induced transport can serve as information router in which the quantum state is prepared at one site of a network and then distributed between multiple users to reduce the complexity of fabrication.

The structure of the paper is as following. In section \[sec2\] the model is introduced, in section \[sec3\] the unrestricted measurement induced dynamics is introduced, in section \[sec4\] the proposal for restricted measurement is discussed and in section \[sec5\] entanglement distribution is analyzed. Then in section \[sec6\] odd chains which do not have SU(2) symmetry are investigated and imperfections are studied in section \[sec7\]. In section \[sec8\] the application of our mechanism in optical lattices is explored. Finally in section \[sec9\] we summarize our results.

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