Using $(448.1pm2.9)times 10^{6}$ $psi(3686)$ events collected with the BESIII detector and a single-baryon tagging technique, we present the first observation of the decays $psi(3686)toXi(1530)^{0}bar{Xi}(1530)^{0}$ and $Xi(1530)^{0}bar{Xi}^0$. The branching fractions are measured to be ${cal{B}}(psi(3686)toXi(1530)^{0}bar{Xi}(1530)^{0}) = (6.77pm0.14pm0.39)times10^{-5}$ and ${cal{B}}(psi(3686)toXi(1530)^{0}bar{Xi}^{0}) = (0.53pm0.04pm0.03)times10^{-5}$. Here, the first and second uncertainties are statistical and systematic, respectively. In addition, the parameter associated with the angular distribution for the decay $psi(3686)toXi(1530)^{0}bar{Xi}(1530)^0$ is determined to be $alpha = 0.32pm0.19pm0.07$, in agreement with theoretical predictions within one standard deviation.
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