True precision limits in quantum metrology

Abstract

We show that quantification of the performance of quantum-enhanced measurement schemes based on the concept of quantum Fisher information yields asymptotically equivalent results as the rigorous Bayesian approach, provided generic uncorrelated noise is present in the setup. At the same time, we show that for the problem of decoherence-free phase estimation this equivalence breaks down and the achievable estimation uncertainty calculated within the Bayesian approach is by a $\pi$ factor larger than that predicted by the QFI even in the large prior knowledge (small parameter fluctuation) regime, where QFI is conventionally regarded as a reliable figure of merit. We conjecture that the analogous discrepancy is present in arbitrary decoherence-free unitary parameter estimation scheme and propose a general formula for the asymptotically achievable precision limit. We also discuss protocols utilizing states with indefinite number of particles and show that within the Bayesian approach it is legitimate to replace the number of particles with the mean number of particles in the formulas for the asymptotic precision, which as a consequence provides another argument that proposals based on the properties of the QFI of indefinite particle number states leading to sub-Heisenberg precisions are not practically feasible.

20 pages, 4 figures

References in corpus (5)

• Reference frames, superselection rules, and quantum information
• Mach-Zehnder Interferometry at the Heisenberg Limit with coherent and squeezed-vacuum light
• General optimality of the Heisenberg limit for quantum metrology
• Phase estimation without a priori knowledge in the presence of loss
• Squeezed vacuum as a universal quantum probe

Cited by in corpus (7)

• Experimental investigation of entropic uncertainty relations and coherence uncertainty relations
• Machine learning \& artificial intelligence in the quantum domain
• Non-asymptotic analysis of quantum metrology protocols beyond the Cramér-Rao bound
• Breaking the weak Heisenberg limit
• Phase sensitivity for an unbalanced interferometer without input phase-matching restrictions
• Parameter estimation in the presence of the most general Gaussian dissipative reservoir
• Probabilistic metrology or how some measurement outcomes render ultra-precise estimates