2014/07/31 by Marcin Jarzyna, Rafał Demkowicz-Dobrzański, Rafal Demkowicz-Dobrzanski · 3 citations
Computer Science · Mathematics · Medicine · Physics and Astronomy · #Applied mathematics #Bayesian probability #Equivalence (formal languages) #Heisenberg limit #Hemodynamic Monitoring and Therapy #Limit (mathematics) #Mathematical analysis #Mathematics #Open quantum system #Physics #Quantum #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum decoherence #Quantum information #Quantum mechanics #Quantum metrology #Quantum technology #Statistical physics #Statistics #Unitary state #quant-ph
paper · pdf · doi:10.1088/1367-2630/17/1/013010
published as New J. Phys. 17, 013010 (2015) · 20 pages, 4 figures
openalex publication_date 2015/01/09 · arxiv created 2015/01/10 · arxiv updated 2015/01/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We show that quantification of the performance of quantum-enhanced measurement schemes based on the concept of quantum Fisher information (QFI) yields results that are asymptotically equivalent to those from 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 larger by a factor of π than that predicted from the QFI even in the large prior knowledge (small parameter fluctuation) regime, where the QFI is conventionally regarded as a reliable figure of merit. We conjecture that an analogous discrepancy is present in the 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 an 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 for proposals based on the properties of the QFI of indefinite particle number states leading to sub-Heisenberg precisions not being practically feasible.