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The error in estimating the separation of a pair of incoherent sources from radiation emitted by them and subsequently captured by an imager is fundamentally bounded below by the inverse of the corresponding quantum Fisher information (QFI) matrix.
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M. Szczykulska, T. Baumgraz, and A. Dutta, “Multi-parameter quantum metrology,” Adv. Physics X, vol. 1, 621-639 (2016)
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Preliminary results appeared in S. Prasad and Z. Yu, “Quantum theory of three-dimensional superresolution using rotating-PSF imagery,” Proc. Advanced Maui Optical and Space Surveillance (AMOS) Technologies Conference (2017), available at https://amostech.com/TechnicalPapers/2017/Adaptive-Optics_Imaging/Prasad.pdf
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D. Safranek, “Simple expression for the quantum Fisher information matrix,” arXiv: 1801.00945 [quant-ph] (2018)
2018
Closest in time.
M. Backlund, Y. Shechtman, and R. Walsworth, “Fundamental precision bounds for three-dimensional optical localization microscopy with Poisson statistics,” Phys. Rev. Lett. 121
2018
Closest in time.
2018
Closest in time.
C. Napoli, T. Tufarelli, S. Piano, R. Leach, and G. Adesso, “Towards superresolution surface metrology: Quantum estimation of angular and axial separations,” submitted to Phys. Rev. Lett., May 2018. In its preliminary version, the work appears on arXiv at arXiv:1805:04116 [quant-ph] (10 May 2018)
2018
Closest in time.