  We show that the teleportation protocol can be efficiently used to detect
quantum critical points using finite temperature data even if all resources
needed to its implementation lie within the system under investigation.
Contrary to a previous proposal, there is no need to use an external qubit as
the input state to be teleported to one of the qubits within the system. Here,
we use a pair of nearest neighbor spins from an infinite spin-1/2 chain in
equilibrium with a heat bath as the entangled resource of the quantum
teleportation protocol and a third adjacent qubit within the chain itself as
the input state to be teleported. For several spin chain models subjected to an
external magnetic field, we show that the efficiency of the teleportation
protocol is severely affected as we cross the quantum critical points
associated with those spin chains. This abrupt change in efficiency gives us a
clear indication of a quantum phase transition.
