ground state just as Ref. [@bayat-xxz]. The results have been given in TABLE I and as it is clear from the data the projective mechanism gives higher fidelity in comparison to the attaching scenarios. The same sort of improvement is observed for the unrestricted projective measurement (not shown in the TABLE I).

Entanglement Distribution {#sec5}
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The proposed measurement induced dynamics for state transfer can also be used for entanglement distribution. To fulfill such task we consider two independent chains which do not interact with each other as shown in Fig. \[fig1\](b). Initially both chains are prepared in their ground states and hence the quantum state of the system is $|GS\ra_L \otimes |GS\ra_R$. A Bell measurement is performed on the first spins of both chains which projects them on one of the following four possible maximally entangled Bell states $$\begin{aligned}
 \label{Bell_states}
  |B_0\ra &=& \frac{|\uparrow\downarrow\ra-|\downarrow\uparrow\ra}{\sqrt{2}} \cr
  |B_1\ra &=& \frac{|\uparrow\downarrow\ra+|\downarrow\uparrow\ra}{\sqrt{2}} \cr
  |B_2\ra &=& \frac{|\uparrow\uparrow\ra-|\downarrow\downarrow\ra}{\sqrt{2}} \cr
  |B_3\ra &=& \frac{|\uparrow\uparrow\ra+|\downarrow\downarrow\ra}{\sqrt{2}}\end{aligned}$$ Since the two chains do not interact any of these four possible outcomes will occur with the probability of 1/4. The symmetry of the system implies that the final entanglement is the same for all of them and thus we assume that the outcome 