Hamiltonian extensions in quantum metrology

TL;DR

This paper investigates whether extending the Hamiltonian with ancillas and interactions can improve phase estimation sensitivity in quantum metrology, concluding that it cannot enhance the quantum Fisher information.

Contribution

It provides a general proof that Hamiltonian extensions do not improve phase estimation sensitivity in quantum metrology.

Findings

Hamiltonian extensions do not increase quantum Fisher information.

The framework encompasses open quantum systems and non-linear metrology.

Extensions cannot surpass the fundamental sensitivity limits.

Abstract

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.