2012/01/31 by Rafał Demkowicz-Dobrzański, Rafal Demkowicz-Dobrzanski, Jan Kołodyński +3 · 10 citations
Computer Science · Mathematics · Physics and Astronomy · #Advanced Frequency and Time Standards #Dephasing #Heisenberg limit #Limit (mathematics) #Mathematics #Metrology #Open quantum system #Photon #Physics #Quantum #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum decoherence #Quantum information #Quantum limit #Quantum mechanics #Quantum metrology #Quantum network #Quantum sensor #Quantum technology #Statistical physics #Upper and lower bounds #quant-ph
paper · pdf · doi:10.1038/ncomms2067
published as Nature Communications 3, 1063 (2012) · 10 pages, 4 figures, presentation imporved, implementation of the semi-definite program finding the precision bounds added
arxiv created 2012/07/03 · openalex publication_date 2012/09/18 · arxiv updated 2012/09/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
Quantum precision enhancement is of fundamental importance for the development of advanced metrological optical experiments, such as gravitational wave detection and frequency calibration with atomic clocks. Precision in these experiments is strongly limited by the 1/√N shot noise factor with N being the number of probes (photons, atoms) employed in the experiment. Quantum theory provides tools to overcome the bound by using entangled probes. In an idealized scenario this gives rise to the Heisenberg scaling of precision 1/N. Here we show that when decoherence is taken into account, the maximal possible quantum enhancement in the asymptotic limit of infinite N amounts generically to a constant factor rather than quadratic improvement. We provide efficient and intuitive tools for deriving the bounds based on the geometry of quantum channels and semi-definite programming. We apply these tools to derive bounds for models of decoherence relevant for metrological applications including: depolarization, dephasing, spontaneous emission and photon loss. Quantum metrology employs the properties of quantum states to further enhance the accuracy of some of the most precise measurement schemes to date. Here, a method for estimating the upper bounds to achievable precision in quantum-enhanced metrology protocols in the presence of decoherence is presented.