Title: Channel Simulation in Quantum Metrology,
Abstract: In this review we discuss how channel simulation can be used to simplify the
most general protocols of quantum parameter estimation, where unlimited
entanglement and adaptive joint operations may be employed. Whenever the
unknown parameter encoded in a quantum channel is completely transferred in an
environmental program state simulating the channel, the optimal adaptive
estimation cannot beat the standard quantum limit. In this setting, we
elucidate the crucial role of quantum teleportation as a primitive operation
which allows one to completely reduce adaptive protocols over suitable
teleportation-covariant channels and derive matching upper and lower bounds for
parameter estimation. For these channels, we may express the quantum Cramér
Rao bound directly in terms of their Choi matrices. Our review considers both
discrete- and continuous-variable systems, also presenting some new results for
bosonic Gaussian channels using an alternative sub-optimal simulation. It is an
open problem to design simulations for quantum channels that achieve the
Heisenberg limit.