• Chinese Optics Letters
  • Vol. 21, Issue 8, 082701 (2023)
Miao Cai1, Zhi-Xiang Li1, Hao-Dong Wu1, Ya-Ping Ruan1, Lei Tang1, Jiang-Shan Tang1, Ming-Yuan Chen1, Han Zhang1、2, Ke-Yu Xia1、4、5、*, Min Xiao1、2、3, and Yan-Qing Lu1
Author Affiliations
  • 1College of Engineering and Applied Sciences, National Laboratory of Solid State Microstructures, Nanjing University, Nanjing 210023, China
  • 2School of Physics, Nanjing University, Nanjing 210023, China
  • 3Department of Physics, University of Arkansas, Fayetteville, Arkansas 72701, USA
  • 4Hefei National Laboratory, Hefei 230088, China
  • 5Jiangsu Key Laboratory of Artificial Functional Materials, Nanjing University, Nanjing 210023, China
  • show less
    DOI: 10.3788/COL202321.082701 Cite this Article Set citation alerts
    Miao Cai, Zhi-Xiang Li, Hao-Dong Wu, Ya-Ping Ruan, Lei Tang, Jiang-Shan Tang, Ming-Yuan Chen, Han Zhang, Ke-Yu Xia, Min Xiao, Yan-Qing Lu. Surpassing the standard quantum limit of optical imaging via deep learning[J]. Chinese Optics Letters, 2023, 21(8): 082701 Copy Citation Text show less

    Abstract

    The sensitivity of optical measurement is ultimately constrained by the shot noise to the standard quantum limit. It has become a common concept that beating this limit requires quantum resources. A deep-learning neural network free of quantum principle has the capability of removing classical noise from images, but it is unclear in reducing quantum noise. In a coincidence-imaging experiment, we show that quantum-resource-free deep learning can be exploited to surpass the standard quantum limit via the photon-number-dependent nonlinear feedback during training. Using an effective classical light with photon flux of about 9×104 photons per second, our deep-learning-based scheme achieves a 14 dB improvement in signal-to-noise ratio with respect to the standard quantum limit.
    r=s+p(s)+n,

    View in Article

    fθtrained=argminθi[fθ(rinput)rtarget]2,

    View in Article

    fθtrained=argminθi{fθ[s+pinput(s)+ninput][s+ptarget(s)+ntarget]}2.

    View in Article

    fθtrained[s+pinput(s)+ninput]E[s+ptarget(s)+ntarget]s,

    View in Article

    rm(l,q)=PPoisson[Nm·Ppattern(l,q)],

    View in Article

    fθtrained[rm(l,q)]=Poutput[Nm·Ppattern(l,q)].

    View in Article

    Nshot=G×F×ηϕpΔte,

    View in Article

    SNR(1)=10lg(Psignal/σnoise2),

    View in Article

    SNR(2)=10lg(Psignal/σsignal2),

    View in Article

    Miao Cai, Zhi-Xiang Li, Hao-Dong Wu, Ya-Ping Ruan, Lei Tang, Jiang-Shan Tang, Ming-Yuan Chen, Han Zhang, Ke-Yu Xia, Min Xiao, Yan-Qing Lu. Surpassing the standard quantum limit of optical imaging via deep learning[J]. Chinese Optics Letters, 2023, 21(8): 082701
    Download Citation