Deep-learning-based quantum imaging using NOON states

The phase sensitivity of photonic NOON states scales O(1/N), which reaches the Heisenberg limit and indicates a great potential in high-quality optical phase sensing. However, the NOON states with large photon number N are experimentally difficult both to prepare and to operate. Such a fact severely limits their practical use. In this article, we soften the requirements for high-quality imaging based on NOON states with large N by introducing deep-learning methods. Specifically, we show that, with the help of deep-learning network, the fluctuation of the images obtained by the NOON states when N = 2 can be reduced to that of the currently infeasible imaging by the NOON states when N = 8. We numerically investigate our results obtained by two types of deep-learning models - deep neural network and convolutional denoising autoencoders, and characterize the imaging quality using the root mean square error. By comparison, we find that small-N NOON state imaging data is sufficient for training the deep-learning models of our schemes, which supports its direct application to the imaging processes.