Quantum limits of localisation microscopy
arXiv:1907.11657 · doi:10.1088/1367-2630/ab58a0
Abstract
We show that localisation microscopy of multiple weak, incoherent point sources with possibly different intensities in one spatial dimension is equivalent to estimating the amplitudes of a classical mixture of coherent states of a simple harmonic oscillator. This enables us to bound the multi-parameter covariance matrix for an unbiased estimator for the locations in terms of the quantum Fisher information matrix, which we obtained analytically. In the regime of arbitrarily small separations we find it to be no more than rank two -- implying that no more than two independent parameters can be estimated irrespective of the number of point sources. We use the eigenvalues of the classical and quantum Fisher information matrices to compare the performance of spatial-mode demultiplexing and direct imaging in localisation microscopy with respect to the quantum limits.
arXiv commentPublished version
References in corpus (25)
- Quantum Theory of Superresolution for Two Incoherent Optical Point Sources
- Compatibility in Multiparameter Quantum Metrology
- A new approach to the Cramer-Rao type bound of the pure state model
- Far-field Superresolution of Thermal Electromagnetic Sources at the Quantum Limit
- Multiparameter Quantum Metrology of Incoherent Point Sources: Towards Realistic Superresolution
- Ultimate precision bound of quantum and sub-wavelength imaging
- A modern description of Rayleigh's criterion
- Local asymptotic normality for finite dimensional quantum systems
- Beating the Rayleigh Limit Using Two-Photon Interference
- Subdiffraction incoherent optical imaging via spatial-mode demultiplexing
- Quantum limit for two-dimensional resolution of two incoherent optical point sources
- Quantum-limited time-frequency estimation through mode-selective photon measurement
- Quantum limit to subdiffraction incoherent optical imaging
- Interferometric superlocalization of two incoherent optical point sources
- Quantum-limited estimation of the axial separation of two incoherent point sources
- Towards superresolution surface metrology: Quantum estimation of angular and axial separations
- Fundamental precision bounds for three-dimensional optical localization microscopy with Poisson statistics
- Quantum limited superresolution of an incoherent source pair in three dimensions
- Fisher information for far-field linear optical superresolution via homodyne or heterodyne detection in a higher-order local oscillator mode
- Optimal measurements for quantum spatial superresolution
- On superresolution imaging as a multiparameter estimation problem
- Subdiffraction incoherent optical imaging via spatial-mode demultiplexing: semiclassical treatment
- Attaining the quantum limit of super resolution in imaging an object's length via pre-detection spatial mode sorting
- Realistic sub-Rayleigh imaging with phase-sensitive measurements
- Non-Orthogonal Bases for Quantum Metrology
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- Discrimination and estimation of incoherent sources under misalignment
- Beyond coincidence: using all the data in Hong-Ou-Mandel interferometry
- Fundamental limits of pulsed quantum light spectroscopy: Dipole moment estimation
- Quantum-limited Localisation and Resolution in Three Dimensions
- Entanglement Enhanced Estimation of a Parameter Embedded in Multiple Phases
- Quantum limit to subdiffraction incoherent optical imaging. II. A parametric-submodel approach
- Imaging arbitrary incoherent source distributions with near quantum-limited resolution
- Quantum limits of parameter estimation in long-baseline imaging
- Super-Resolution Imaging with Multiparameter Quantum Metrology in Passive Remote Sensing
- Physics-inspired forms of the Bayesian Cramér-Rao bound
- Generalization of Rayleigh's Criterion on Parameter Estimation with Incoherent Sources
- On the role of chirping in pulsed single photon spectroscopy
- Efficient superoscillation measurement for incoherent optical imaging
- Optimizing measurement tradeoffs in multiparameter spatial superresolution
- Off-axis Aberrations Improve the Resolution Limits of Incoherent Imaging
- Quantum limit to subdiffraction incoherent optical imaging. III. Numerical analysis
- Joint Estimation of a Two-Phase Spin Rotation beyond Classical Limit
- Tight information bounds for spontaneous emission lifetime resolution of quantum sources with varied spectral purity
- Breaking Rayleigh's curse for two unbalanced single-photon emitters: BLESS technique
- Cascaded Multiparameter Quantum Metrology
- Quantum resolution limit of long-baseline imaging using distributed entanglement
- Performance advantage of discriminating one-versus-two incoherent sources based on quantum hypothesis testing
- Quantum-limited superresolution of two arbitrary incoherent point sources: beating the resurgence of Rayleigh's curse
- Efficient estimation of error bounds for quantum multiparametric imaging with constraints
- Weak convexity of Fisher information matrix and superresolved localization of blinking sources of light
- Quantum limits to resolution and discrimination of spontaneous emission lifetimes
- Quantifying classical and quantum bounds for resolving closely spaced, non-interacting, simultaneously emitting dipole sources in optical microscopy
- Multiparameter quantum estimation with Gaussian states: efficiently evaluating Holevo, RLD and SLD Cramér-Rao bounds
- Quantum-enhanced passive remote sensing