Hamiltonian extensions in quantum metrology

Understand

We study very generally to what extent the uncertainty with which a phase shift can be estimated in quantum metrology can be reduced by extending the Hamiltonian that generates the phase shift to an ancilla system with a Hilbert space of arbitrary dimension, and allowing arbitrary interactions between the original system and the ancilla.

• Such Hamiltonian extensions provide a general framework for open quantum systems, as well as for "non-linear metrology schemes" that have been investigated over the last few years.
• We prove that such Hamiltonian extensions cannot improve the sensitivity of the phase shift measurement when considering the quantum Fisher information optimized over input states.