Generalized Limits for Single-Parameter Quantum Estimation

Abstract

We develop generalized bounds for quantum single-parameter estimation problems for which the coupling to the parameter is described by intrinsic multisystem interactions. For a Hamiltonian with $k$-system parameter-sensitive terms, the quantum limit scales as $1/N^k$, where $N$ is the number of systems. These quantum limits remain valid when the Hamiltonian is augmented by any parameter-independent interaction among the systems and when adaptive measurements via parameter-independent coupling to ancillas are allowed.