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Using the ORCA 5.0.2 software package we have simulated for a first time the full tensors nJKL (K,L=X,Y,Z), describing n-bond J-coupling of nuclear spins 13C in H-terminated diamond-like clusters C10H16 (adamantane) and C35H36 as well as in the cluster C33[NV-]H36 hosting the negatively charged NV- center. We found that, in addition to usually considered isotropic scalar nJ-coupling constant the anisotropic contributions to the nJ-coupling tensor are essential. We have also shown that the presence of the NV center affects the J-coupling characteristics, especially in the case of 13C-13C pairs located near the vacancy of the NV center., Comment: 10 pages, 3 figures, proceeding paper IOCN2022

Quantum imaging can beat classical resolution limits, imposed by diffraction of light. In particular, it is known that one can reduce the image blurring and increase the achievable resolution by illuminating an object by entangled light and measuring coincidences of photons. If an $n$-photon entangled state is used and the $n$th-order correlation function is measured, the point-spread function (PSF) effectively becomes $\sqrt n$ times narrower relatively to classical coherent imaging. Quite surprisingly, measuring $n$-photon correlations is not the best choice if an $n$-photon entangled state is available. We show that for measuring $(n-1)$-photon coincidences (thus, ignoring one of the available photons), PSF can be made even narrower. This observation paves a way for a strong conditional resolution enhancement by registering one of the photons outside the imaging area. We analyze the conditions necessary for the resolution increase and propose a practical scheme, suitable for observation and exploitation of the effect.

Here, we show that, contrary to the common opinion, the super-resolution optical fluctuation microscopy might not lead to ideally infinite super-resolution enhancement with increasing of the order of measured cumulants. Using information analysis for estimating error bounds on the determination of point sources positions, we show that reachable precision per measurement might be saturated with increasing of the order of the measured cumulants in the super-resolution regime. In fact, there is an optimal correlation order beyond which there is practically no improvement for objects of three and more point sources. However, for objects of just two sources, one still has an intuitively expected resolution increase with the cumulant order.

Quantum imaging has a potential of enhancing precision of the object reconstruction by using quantum correlations of the imaging field. This is especially important for imaging requiring low-intensity fields up to the level of few-photons. However, quantum imaging generally leads to nonlinear estimation problems. The complexity of these problems rapidly increases with the number of parameters describing the object. We suggest a way to drastically reduce the complexity for a wide class of problems. The key point of our approach is connecting the features of the Fisher information with the parametric locality of the problem, and building the efficient iterative inference scheme reconstructing only a subset of the whole set of parameters in each step. This iterative scheme is linear on the total number of parameters. This scheme is applied to quantum near-field imaging, the inference procedure is developed resulting in super-resolving reconstruction of grey compound transmission objects. The functionality of the method is demonstrated with experimental data obtained by measurements of higher-order correlation functions for imaging with entangled twin-photons and pseudo-thermal light sources. By analyzing the informational content of the measurement, it becomes possible to predict the existence of optimal photon correlations providing for the best image resolution in the super-resolution regime. This prediction is experimentally confirmed. It is also shown how an estimation bias stemming from image features may drastically improve the resolution.