Generalized Limits for Single Quantum Parameter Estimation

Sergio Boixo, Steven T. Flammia, Carlton M. Caves, and JM Geremia
Department of Physics and Astronomy, The University of New Mexico, Albuquerque NM 87131 USA

Abstract. We develop generalized bounds for quantum single-parameter estimation problems for which the coupling to the parameter is described by intrinsic multi-system 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.

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