INFN Sez. Pavia

Quantum technologies promise breakthroughs in how we sense, measure, and interact with the world. At the heart of this revolution lies quantum metrology: the science of making ultraprecise measurements using the unique features of quantum systems, such as entanglement and superposition. But in realistic settings, quantum systems are noisy, and their precision is often limited by the practical constraints of time and energy.

Assuming Markovian time evolution of a quantum sensing system, we study the general characterization of the optimal sensitivity scalings with time, under most general quantum control protocols. We allow the estimated parameter to influence both the Hamiltonian as well as the dissipative part of the quantum master equation and focus on the asymptotic-time along with the short-time sensitivity scalings.

We give two upper bounds to the mutual information in arbitrary quantum estimation strategies. The first is based on some simple Fourier properties of the estimation apparatus. The second is derived using the first, but, interestingly, depends only on the Fisher information of the parameter, so it is valid even beyond quantum estimation. We illustrate the usefulness of these bounds by characterizing the quantum phase estimation algorithm in the presence of noise.