Quantum-optimal detection of one-versus-two incoherent optical sources with arbitrary separation
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Lu, X. M., Krovi, H., Nair, R., Guha, S., & Shapiro, J. H. (2018). Quantum-optimal detection of one-versus-two incoherent optical sources with arbitrary separation. npj Quantum Information, 4(1), 1-8.Journal
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© The Author(s) 2018. This article is licensed under a Creative Commons Attribution 4.0 International License.Collection Information
This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at repository@u.library.arizona.edu.Abstract
We analyze the fundamental quantum limit of the resolution of an optical imaging system from the perspective of the detection problem of deciding whether the optical field in the image plane is generated by one incoherent on-axis source with brightness. or by two epsilon/2-brightness incoherent sources that are symmetrically disposed about the optical axis. Using the exact thermal-state model of the field, we derive the quantum Chernoff bound for the detection problem, which specifies the optimum rate of decay of the error probability with increasing number of collected photons that is allowed by quantum mechanics. We then show that recently proposed linear-optic schemes approach the quantum Chernoff bound-the method of binary spatial-mode demultiplexing (B-SPADE) is quantum-optimal for all values of separation, while a method using image inversion interferometry (SLIVER) is near-optimal for sub-Rayleigh separations. We then simplify our model using a low-brightness approximation that is very accurate for optical microscopy and astronomy, derive quantum Chernoff bounds conditional on the number of photons detected, and show the optimality of our schemes in this conditional detection paradigm. For comparison, we analytically demonstrate the superior scaling of the Chernoff bound for our schemes with source separation relative to that of spatially resolved direct imaging. Our schemes have the advantages over the quantum-optimal (Helstrom) measurement in that they do not involve joint measurements over multiple modes, and that they do not require the angular separation for the two-source hypothesis to be given a priori and can offer that information as a bonus in the event of a successful detection.Note
Open access journalEISSN
2056-6387Version
Final published versionSponsors
Zhejiang Provincial Natural Science Foundation of China [LY18A050003]; National Natural Science Foundation of China [61871162, 11805048]; Singapore National Research Foundation [NRF-NRFF2011-07]; Singapore Ministry of Education Academic Research Fund [R-263-000-C06-112]; Defense Advanced Research Projects Agency's (DARPA) Information in a Photon (InPho) program [HR0011-10-C-0159]; REVEAL and EXTREME Imaging program; Air Force Office of Scientific Research [FA9550-14-1-0052]ae974a485f413a2113503eed53cd6c53
10.1038/s41534-018-0114-y
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Except where otherwise noted, this item's license is described as © The Author(s) 2018. This article is licensed under a Creative Commons Attribution 4.0 International License.