  We argue that long optical storage times are required to establish
entanglement at high rates over large distances using memory-based quantum
repeaters. Triggered by this conclusion, we investigate the $^3$H$_6$
$\leftrightarrow$ $^3$H$_4$ transition at 795.325 nm of Tm:Y$_3$Ga$_5$O$_{12}$
(Tm:YGG). Most importantly, we show that the optical coherence time can reach
1.1 ms, and, using laser pulses, we demonstrate optical storage based on the
atomic frequency comb protocol up to 100 $\mu$s as well as a memory decay time
T$_M$ of 13.1 $\mu$s. Possibilities of how to narrow the gap between the
measured value of T$_m$ and its maximum of 275 $\mu$s are discussed. In
addition, we demonstrate quantum state storage using members of non-classical
photon pairs. Our results show the potential of Tm:YGG for creating quantum
memories with long optical storage times, and open the path to building
extended quantum networks.

Quantum Physics;Applied Physics;Optics