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Quantum teleportation between two quantum spin Hall insulator rings

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.