Robust state transfer in the quantum spin channel via weak measurement and quantum measurement reversal

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Using the weak measurement (WM) and quantum measurement reversal (QMR) approach, robust state transfer and entanglement distribution can be realized in the spin-$\frac{1}{2}$ Heisenberg chain. We find that the ultrahigh fidelity and long distance of quantum state transfer with certain success probability can be obtained using proper WM and QMR, i.e., the average fidelity of a general pure state from $80%$ to almost $100%$, which is almost size independent. We also find that the distance and quality of entanglement distribution for the Bell state and the general Werner mixed state can be obviously improved by the WM and QMR approach.