Surpassing the standard quantum limit of optical imaging via deep learning

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 × 10 4 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.