  We consider the estimation of noise parameters in a quantum channel, assuming
the most general strategy allowed by quantum mechanics. This is based on the
exploitation of unlimited entanglement and arbitrary quantum operations, so
that the channel inputs may be interactively updated. In this general scenario
we draw a novel connection between quantum metrology and teleportation. In
fact, for any teleportation-covariant channel (e.g., Pauli, erasure, or
Gaussian channel), we find that adaptive noise estimation cannot beat the
standard quantum limit, with the quantum Fisher information being determined by
the channel's Choi matrix. As an example, we establish the ultimate precision
for estimating excess noise in a thermal-loss channel which is crucial for
quantum cryptography. Because our general methodology applies to any functional
which is monotonic under trace-preserving maps, it can be applied to simplify
other adaptive protocols, including those for quantum channel discrimination.
Setting the ultimate limits for noise estimation and discrimination paves the
way for exploring the boundaries of quantum sensing, imaging and tomography.
