Quantum limits of superresolution in a noisy environment

Abstract

We analyze the ultimate quantum limit of resolving two identical sources in a noisy environment. We prove that in the presence of noise causing false excitation, such as thermal noise, the quantum Fisher information of arbitrary quantum states for the separation of the objects, which quantifies the resolution, always converges to zero as the separation goes to zero. Noisy cases contrast with a noiseless case where it has been shown to be nonzero for a small distance in various circumstances, revealing the superresolution. In addition, we show that false excitation on an arbitrary measurement, such as dark counts, also makes the classical Fisher information of the measurement approach to zero as the separation goes to zero. Finally, a practically relevant situation resolving two identical thermal sources, is quantitatively investigated by using the quantum and classical Fisher information of finite spatial mode multiplexing, showing that the amount of noise poses a limit on the resolution in a noisy system.

12 pages, 2 figures

References in corpus (6)

• Multiparameter Quantum Metrology of Incoherent Point Sources: Towards Realistic Superresolution
• Subdiffraction incoherent optical imaging via spatial-mode demultiplexing
• Fisher information for far-field linear optical superresolution via homodyne or heterodyne detection in a higher-order local oscillator mode
• Superresolution Limits from Measurement Crosstalk
• Optimal measurements for quantum fidelity between Gaussian states and its relevance to quantum metrology
• Subwavelength quantum imaging with noisy detectors

Cited by in corpus (26)

• Super-resolution linear optical imaging in the far field
• Quantum hypothesis testing for exoplanet detection
• Optical-domain spectral super-resolution via a quantum-memory-based time-frequency processor
• Optimal observables and estimators for practical superresolution imaging
• Moment-based superresolution: Formalism and applications
• Measurement noise susceptibility in quantum estimation
• Back to sources -- the role of losses and coherence in super-resolution imaging revisited
• Poisson Quantum Information
• Imaging arbitrary incoherent source distributions with near quantum-limited resolution
• Application range of crosstalk-affected spatial demultiplexing for resolving separations between unbalanced sources
• Super-Resolution Imaging with Multiparameter Quantum Metrology in Passive Remote Sensing
• Evaluating the quantum Ziv-Zakai bound in noisy environments
• Sub-Rayleigh characterization of a binary source by spatially demultiplexed coherent detection
• Super-resolution of ultrafast pulses via spectral inversion
• Quantum thermometry in diffraction-limited systems
• Tight information bounds for spontaneous emission lifetime resolution of quantum sources with varied spectral purity
• Machine learning with sub-diffraction resolution in the photon-counting regime
• Lindblad estimation with fast and precise quantum control
• Quantum-limited superresolution of two arbitrary incoherent point sources: beating the resurgence of Rayleigh's curse
• Performance advantage of quantum hypothesis testing for partially coherent optical sources
• Estimating quantum Markov chains using coherent absorber post-processing and pattern counting estimator
• Performance advantage of discriminating one-versus-two incoherent sources based on quantum hypothesis testing
• Quantum-inspired exoplanet detection in the presence of experimental imperfections
• Impact of the Unruh effect on the estimation precision of Gaussian channel parameters
• Quantum-enhanced passive remote sensing
• Quantum Metrology under Coarse-Grained Measurement