Heisenberg scaling in Gaussian quantum metrology

Understand

We address the issue of precisely estimating small parameters encoded in a general linear transformation of the modes of a bosonic quantum field.

• Such Bogoliubov transformations frequently appear in the context of quantum optics.
• We provide a set of instructions for computing the quantum Fisher information for arbitrary pure initial states.
• We show that the maximally achievable precision of estimation is inversely proportional to the squared average particle number and that such Heisenberg scaling requires non-classical, but not necessarily entangled states.