( Quantum) FISHER INFORMATION FOCUS
dependence on the parameter of interest is known [ 10 ]. One practical example is MINFLUX [ 8 ], which improves the localization of fluorophores using an excitation beam that features an intensity zero, and that sequentially illuminates various spots within a region of characteristic size L. The CRB of MINFLUX scales as L / √— N d, which is independent of the diffraction limit. Furthermore,“ iterative” MINFLUX [ 9 ] dynamically reduces L as photons are collected, enhancing the localization precision. Doing so in K steps yields an overall CRB scaling of L / N d
K / 2
, which can beat the QCRB of non-adaptive schemes( see Fig 1D). MINFLUX typically reaches an isotropic CRB of σ x, y, z / λ≈0.06 / √— N d.
CONCLUSION Treating microscopy as a parameter estimation task allows us to systematically benchmark and optimise imaging schemes based on rigorous statistical quantities. Does the error in my position estimate of a specimen reach the
CRB for my measurement scheme? Does the FI of my measurement scheme reach the QFI of the probe state? These are questions every experimentalist can use to optimize the experiment. However, reaching the QCRB should not be seen as a final step. We discussed how the clever interferometric design in iScat yields an axial QCRB far better than other axial localization techniques. We have also seen how shaping the incoming light can yield better QCRBs, and how adaptive measurements in MINFLUX can even bypass the 1 / N scaling of the QCRB. Further pathways to increased QFI can be found using quantum resources [ 1 ], such as entangled or squeezed states, or cavity-enhanced imaging [ 11 ]. Including prior knowledge can further guide the design and analysis of experiments and drastically improve results. We thus conclude that, as with many ultimate or fundamental bounds, it is important to know the underlying assumptions and to search for ways to overcome them.
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