  Quantum repeater networks are a fundamental of any future quantum Internet
and long-distance quantum communications. The entangled quantum nodes can
communicate through several different levels of entanglement, leading to a
heterogeneous, multi-level network structure. The level of entanglement between
the quantum nodes determines the hop distance and the probability of the
existence of an entangled link in the network. Here, we define a decentralized
routing for entangled quantum networks. The proposed method allows an efficient
routing to find the shortest paths in entangled quantum networks by using only
local knowledge of the quantum nodes. We give bounds on the maximum value of
the total number of entangled links of a path. The proposed scheme can be
directly applied in practical quantum communications and quantum networking
scenarios.
