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