Our latest work on quantum conditional expectations is published in Quantum:

This work is a continuation of the following:

I gave a talk on the basic idea at the University of Toronto on Nov 10; the recording is here:

https://www.youtube.com/watch?v=dAkvLLvhlTw

and the slides are here:

https://drive.google.com/file/d/1GpNSbcrr-MI7cTqkTY32nWYck76mdGe6/view?usp=drive_link

1. “Resolving starlight: a quantum perspective,” CQIQC/QO/AMO Seminar, University of Toronto, Canada, Oct 20, 2023: https://www.youtube.com/watch?v=458pYv8QVtE. [Slides PDF]
2. “Quantum waveform estimation, detection, and noise spectroscopy,” KITP Conference “Frontiers of Quantum Metrology,” UCSB, USA, Oct 12, 2023: https://online.kitp.ucsb.edu/online/qmetro-c23/tsang/. [Slides PDF]

A recording of my seminar “Resolving starlight: a quantum perspective” at the Kavli Institute for Theoretical Physics (KITP), University of California-Santa Barbara (under the program “New Directions in Quantum Metrology“) on 13 Sep, 2023 is here:

https://online.kitp.ucsb.edu/online/qmetro23/tsang/

The slides can be found at the website above or here.

Xiao-Jie Tan, Luo Qi, Lianwei Chen, Aaron J. Danner, Pakorn Kanchanawong, and Mankei Tsang, “Quantum-inspired superresolution for incoherent imaging,” Optica 10, 1189-1194 (2023). [Open Access]

Experiment on quantum-inspired superresolution by our student Xiao-Jie Tan and postdoc Luo Qi. Using spatial-mode demultiplexing (SPADE), we demonstrate that we are able to find the locations of two subdiffraction point sources accurately, not just their separation. For extended objects that consist of multiple point sources, we also demonstrate that we are able to estimate their properties in terms of the moments.

Still very classical and proof-of-concept, but Luo Qi and Xiao-Jie Tan are working hard to demonstrate something more significant in the next few months.

Mankei Tsang, “Efficient superoscillation measurement for incoherent optical imaging,” IEEE Journal of Selected Topics in Signal Processing 11, 513-524 (2023) [arXiv PDF].

This work relates our previous works on moment estimation to the estimation of generalized Fourier coefficients in the context of superoscillation. A step towards a general quantum theory of image reconstruction.

Mankei Tsang, “Quantum noise spectroscopy as an incoherent imaging problem,” Physical Review A 107, 012611 (2023) [arXiv PDF].

People often asked us whether we can apply our quantum-inspired superresolution ideas to gravitational-wave detection. This paper shows that the answer is yes, if the goal is to detect a stochastic gravitational-wave background. This is because the two problems have the same random displacement model under the hood: randomly displaced photons in the case of imaging, and randomly displaced fields in the case of optomechanical detector. With the correspondence direct imaging = homodyne, SPADE = photon counting in the spectral modes, photon counting turns out to be far superior to homodyne in the same way SPADE is superior.