Quantum limit to subdiffraction incoherent optical imaging. II. A parametric-submodel approach
arXiv:2010.03518 · doi:10.1103/PhysRevA.104.052411
Abstract
In a previous paper [M. Tsang, Phys. Rev. A 99, 012305 (2019)], I proposed a quantum limit to the estimation of object moments in subdiffraction incoherent optical imaging. In this sequel, I prove the quantum limit rigorously by infinite-dimensional analysis. A key to the proof is the choice of an unfavorable parametric submodel to give a bound for the semiparametric problem. By generalizing the quantum limit for a larger class of moments, I also prove that the measurement method of spatial-mode demultiplexing (SPADE) with just one or two modes is able to achieve the quantum limit. For comparison, I derive a classical bound for direct imaging using the parametric-submodel approach, which suggests that direct imaging is substantially inferior.
arXiv comment17 pages, 4 figures. v4: corrected minor typos. Published
References in corpus (25)
- General framework for estimating the ultimate precision limit in noisy quantum-enhanced metrology
- Quantum limits in optical interferometry
- Quantum Theory of Superresolution for Two Incoherent Optical Point Sources
- Modes and states in Quantum Optics
- A modern description of Rayleigh's criterion
- Resolving starlight: a quantum perspective
- Subdiffraction incoherent optical imaging via spatial-mode demultiplexing
- Quantum limit to subdiffraction incoherent optical imaging
- Quantum Semiparametric Estimation
- Super-resolution linear optical imaging in the far field
- Subdiffraction incoherent optical imaging via spatial-mode demultiplexing: semiclassical treatment
- Quantum limits of localisation microscopy
- General expressions for the quantum Fisher information matrix with applications to discrete quantum imaging
- Attaining the quantum limit of super resolution in imaging an object's length via pre-detection spatial mode sorting
- Spectrum analysis with quantum dynamical systems
- One from many: Estimating a function of many parameters
- Conservative classical and quantum resolution limits for incoherent imaging
- Realistic sub-Rayleigh imaging with phase-sensitive measurements
- Semiparametric estimation for incoherent optical imaging
- Confocal super-resolution microscopy based on a spatial mode sorter
- Coherence effects on estimating general sub-Rayleigh object distribution moments
- Quantum-accelerated imaging of N stars
- Poisson Quantum Information
- Quantum Limited Superresolution of Extended Sources in One and Two Dimensions
- Physics-inspired forms of the Bayesian Cramér-Rao bound
Cited by in corpus (5)
- Quantum noise spectroscopy as an incoherent imaging problem
- Back to sources -- the role of losses and coherence in super-resolution imaging revisited
- Efficient superoscillation measurement for incoherent optical imaging
- Semiparametric estimation in Hong-Ou-Mandel interferometry
- Generalized conditional expectations for quantum retrodiction and smoothing