As a breakthrough technology in recent years, super-resolution imaging has become an important research problem in computer vision and image processing and has wide practical applications in medical, biological, security, and other fields. However, classical imaging technology is limited by the diffraction resolution limit, and it is difficult to achieve resolution breakthroughs. Quantum entanglement can transcend diffraction resolution limits by sharpening spatial interference fringes based on quantum technology evolution . The entangled N00N state has been studied because it can exceed the standard quantum limit. The interference visibility of the three-photon N00N state is higher than the limit of classical spatial super-resolution, and the pattern of the N-photon entangled N00N state is N times finer than that of classical light. Thus, the N00N state can improve the resolution of the optical system by N times. However, the probability of all N photons arriving at the same location and the detection efficiency decreases exponentially with increasing N, making the advantages of the N00N state controversial. The optical centroid measurement (OCM) promotes the application of the N00N state in super-resolution imaging. This study further applies the advantages of N-photon entangled N00N state to super-resolution quantum imaging based on existing theories and technologies. This study further proposes a new quantum imaging system to improve the resolution of object imaging.

This study primarily adopts theoretical analysis and simulation methods. A simulation model based on the proposed quantum imaging system is created, and the resolution enhancement of our scheme is quantified by measuring the modulation transfer function (MTF). A photon source model is constructed to generate coherent photons that are irradiated onto the object and transmitted to the receiver. The centroid position of the photons is measured using the OCM method, and the point spread function (PSF) of the imaging system is calculated using the obtained simulation data. Finally, the MTF is obtained using the Fourier transform method. In addition to the theoretical analysis of the detection efficiency enhancement of N00N state by OCM, the advantages of OCM visibility are analyzed through simulation visibility. The data are obtained through model simulation, and the curve is fitted to the data point, following the visibility calculation and analysis using the fitted curve.

The model simulation of the proposed imaging system shows that the MTF curve decreases with the increase of spatial frequency. However, the entangled two-photon curve changes more gently than the spatially uncorrelated two-photon curve, indicating that the resolution of entangled two-photon imaging is better than that of uncorrelated two-photon imaging. Similarly, the presence of more entangled photons changes the curve at a slower pace. The resolution of (16±2)% is enhanced in the two-photon N00N entangled state, and the resolutions of 4 and 8 photons are 30±3%, and 41±2%, respectively (Fig.2 and Table 1). The results verify the feasibility of the OCM imaging scheme for N-photon entangled N00N state super-resolution imaging. Moreover, the resolution can be enhanced by increasing the number of photons. The visibilities obtained by OCM for classical light and N00N entangled light are compared. The visibility decreases significantly as the number of photons of classical light increases from 2 to 4. The visibilities of 2, 3 and 4 photons are 45±5%,17±4%, and 12±2%, respectively, whereas the visibility obtained by OCM for N00N entangled light remains relatively constant. The obtained visibilities of 2, 3, and 4 photons are 50±4%, (44±2)%, and (42±4)%, respectively (Fig.3), achieving improved visibility.

The quantum imaging system scheme presented in this study improves the detection efficiency of N00N state by means of optical centroid measurement, and exploits the N-photon entanglement of N00N state to realize super-resolution imaging of objects. OCM does not require all photons to reach the same point in space as compared to the N-photon absorption scheme. The resolution of any number of photons can be improved by photon counting and proper post-processing, which significantly improves the detection efficiency of N00N entangled states. Moreover, the visibility of the OCM signal in N00N state is almost independent of the change in photon number N; therefore, the imaging system is suitable for higher photon numbers. The super-resolution quantum imaging system based on N-photon entanglement overcomes the problem in effectively detecting N-photon states, which improves quantum-enhanced measurement. Moreover, it is significant for Heisenberg finite phase detection and the development of super-resolution quantum imaging. Theoretically, the system can enhance N-1 times of image resolution. The prepared N00N state has high fidelity and stability. Thus, it is expected to be more commonly applied in research and promote new progress in the field of super-resolution quantum imaging.