Precision bounds for noisy nonlinear quantum metrology

Abstract

We derive the ultimate bounds on the performance of nonlinear measurement schemes in the presence of noise. In particular, we investigate the precision of the second-order estimation scheme in the presence of the two most detrimental types of noise, photon loss and phase diffusion. We find that the second-order estimation scheme is affected by both types of noise in an analogous way as the linear one. Moreover, we observe that for both types of noise the gain in the phase sensitivity with respect to the linear estimation scheme is given by a multiplicative term $\mathcal{O}(1/N)$. Interestingly, we also find that under certain circumstances, a careful engineering of the environment can, in principle, improve the performance of measurement schemes affected by phase diffusion.

9 pages, 2 figures, 1 table, 1 appendix; v3 contains an improved analysis and a stronger precision bound for the case of photon loss; published version

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• Heisenberg versus standard scaling in quantum metrology with Markov generated states and monitored environment
• Evaluating the quantum Ziv-Zakai bound in noisy environments
• Ultimate phase estimation in a squeezed-state interferometer using photon counters with a finite number resolution
• A single atom noise probe operating beyond the Heisenberg limit