The elusive Heisenberg limit in quantum-enhanced metrology

By Rafal Demkowicz-Dobrzanski, J. Kołodyński, Madalin Guta. Nature Communications, 2012

682 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/d1a85cf8ff0d2b33284248bcf0e3b3dcd7e5afb7

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Citations in the corpus

At the limits of criticality-based quantum metrology: apparent super-Heisenberg scaling revisited (2017, background): “Furthermore, let us mention that the final formula is quite sensitive to a local noise, and because of that, one basically always ends up with the classical scaling for large enough N [17].”
Macroscopic quantum states: Measures, fragility, and implementations (2017, background): “34 Demkowicz-Dobrzanski et al. (2012); Escher et al. (2011); Fujiwara and Imai (2008); Sekatski et al. (2016) 35 A. Lopez Incera et al., in preparation.”
Quantum limits in optical interferometry (2014, methodology): “Yet, the general frameworks proposed by (Demkowicz-Dobrzański et al., 2012; Escher et al., 2011) for generic decoherence allowed to reconstruct this bound on precision with the following result: ∆ϕ ≥ 1 2 (√ 1− ηa ηa + √ 1− ηb ηb ) 1√ N , .”