  A quantum teleportation between two quantum spin Hall insulator (QSHI) rings
is proposed. A qubit state is generated in the first QSHI ring and the second
is used as a quantum channel in entangled QSHI state. In the intersection of
outer edges is placed a joint detector, allowing a Bell state analysis. After
the Bell state measurement, Alice, that is composed originally of a qubit in
the first QSHI ring and one spin state in the second QSHI ring, allows Bob,
that is composed of the other spin edge state in the second QSHI ring, to
realize the corresponding control of the tunneling amplitudes in the second
QSHI ring, what implements a complete quantum teleportation between the QSHI
rings. It is also showed that Bob's table, used after the classical
communication by Alice, is the same independently the way the qubit is
generated in the first QSHI ring. This description indicates that a quantum
teleportation can be fully implemented in the context of two-dimensional (2D)
topological edge states and opens perspectives in the scenario of quantum
information in topological matter, decoherence free systems, as well as for the
development of quantum technologies associated to spintronics and quantum
computation.
