  It is commonly believed that the fidelity of quantum teleportation in the
gravitational field would be degraded due to the heat up by the Hawking
radiation. In this paper, we point out that the Hawking effect could be
eliminated by the combined action of pre- and post-weak measurements, and thus
the teleportation fidelity is almost completely protected. It is intriguing to
notice that the enhancement of fidelity could not be attributed to the
improvement of entanglement, but rather to the probabilistic nature of weak
measurements. Our work extends the ability of weak measurements as a quantum
technique to battle against gravitational decoherence in relativistic quantum
information.
