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We relate the principle of quantum-memory-assisted entropic uncertainty toquantum teleportation and show geometrically that any two-qubit state whichlowers the upper bound of this uncertainty relation is useful forteleportation. We also explore the efficiency of this entropic uncertaintyprinciple on witnessing entanglement in a general class of bosonic structuredreservoirs. The entanglement regions witnessed by different estimates aredetermined, which may have no relation with the explicit form of the spectraldensity of the reservoir for certain special chosen sets of the initial states.

Quantum-memory-assisted entropic uncertainty principle, teleportation and entanglement witness in structured reservoirs