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We present a proposal to test Bell inequality in the emerging field of cavity optomagnonics, where a sphere of ferromagnetic crystal supports two optical whispering gallery modes and one magnon mode. The two optical modes are driven by two laser pulses, respectively. Entanglement between magnon mode and one of the two optical modes will be generated by the first pulse, and the state of magnon mode is subsequently mapped into another optical mode via the second pulse. Hence correlated photon-photon pairs is created out of the cavity. A Bell test can be implemented using these pairs, which enables us to test local hidden-variable models at macroscopic optomagnonical system. Our results show that a significant violation of Bell inequality can be obtained in the experimentally relevant weak-coupling regime. The violation of Bell inequality not only verifies the entanglement between magnons and photons, but also implies that cavity optomagnonics is a promising platform for quantum information processing tasks.

This paper aims to devise a generalized maximum likelihood (ML) estimator to robustly detect signals with unknown noise statistics in multiple-input multiple-output (MIMO) systems. In practice, there is little or even no statistical knowledge on the system noise, which in many cases is non-Gaussian, impulsive and not analyzable. Existing detection methods have mainly focused on specific noise models, which are not robust enough with unknown noise statistics. To tackle this issue, we propose a novel ML detection framework to effectively recover the desired signal. Our framework is a fully probabilistic one that can efficiently approximate the unknown noise distribution through a normalizing flow. Importantly, this framework is driven by an unsupervised learning approach, where only the noise samples are required. To reduce the computational complexity, we further present a low-complexity version of the framework, by utilizing an initial estimation to reduce the search space. Simulation results show that our framework outperforms other existing algorithms in terms of bit error rate (BER) in non-analytical noise environments, while it can reach the ML performance bound in analytical noise environments. The code of this paper is available at https://github.com/skypitcher/manfe.

This paper investigates the optimal signal detection problem with a particular interest in large-scale multiple-input multiple-output (MIMO) systems. The problem is NP-hard and can be solved optimally by searching the shortest path on the decision tree. Unfortunately, the existing optimal search algorithms often involve prohibitively high complexities, which indicates that they are infeasible in large-scale MIMO systems. To address this issue, we propose a general heuristic search algorithm, namely, hyper-accelerated tree search (HATS) algorithm. The proposed algorithm employs a deep neural network (DNN) to estimate the optimal heuristic, and then use the estimated heuristic to speed up the underlying memory-bounded search algorithm. This idea is inspired by the fact that the underlying heuristic search algorithm reaches the optimal efficiency with the optimal heuristic function. Simulation results show that the proposed algorithm reaches almost the optimal bit error rate (BER) performance in large-scale systems, while the memory size can be bounded. In the meanwhile, it visits nearly the fewest tree nodes. This indicates that the proposed algorithm reaches almost the optimal efficiency in practical scenarios, and thereby it is applicable for large-scale systems. Besides, the code for this paper is available at \url{https://github.com/skypitcher/hats}.

The Fock-Bargmann-Hartogs domain $D_{n, m}(\mu)$ is defined by $$ D_{n, m}(\mu):=\{(z, w)\in\mathbb{C}^{n}\times\mathbb{C}^m:\Vert w \Vert^20.$ The Fock-Bargmann-Hartogs domain $D_{n, m}(\mu)$ is an unbounded strongly pseudoconvex domain with smooth real-analytic boundary. In this paper, we first compute the weighted Bergman kernel of $D_{n, m}(\mu)$ with respect to the weight $(-\rho)^{\alpha}$, where $\rho(z,w):=\|w\|^2-e^{-\mu \|z\|^2}$ is a defining function for $D_{n, m}(\mu)$ and $\alpha>-1$. Then, for $p\in [1,\infty),$ we show that the corresponding weighted Bergman projection $P_{D_{n, m}(\mu), (-\rho)^{\alpha}}$ is unbounded on $L^p(D_{n, m}(\mu), (-\rho)^{\alpha})$, except for the trivial case $p=2$. In particular, this paper gives an example of an unbounded strongly pseudoconvex domain whose ordinary Bergman projection is $L^p$ irregular when $p\in [1,\infty)\setminus\{2\}$. This result turns out to be completely different from the well-known positive $L^p$ regularity result on bounded strongly pseudoconvex domain.

Ammonia, key precursor for fertilizer production, convenient hydrogen carrier and emerging clean fuel, plays a pivotal role in sustaining life on earth. Currently, the main route for NH3 synthesis is via the heterogeneous catalytic Haber-Bosch process (N2+3H2 - 2NH3), which proceeds under extreme conditions of temperature and pressure with a very large carbon footprint. Herein we report that a pristine nitrogen-doped nanoporous graphitic carbon membrane (NCM) can electrochemically convert N2 into NH3 in an aqueous acidic solution under ambient conditions. The Faradaic efficiency and rate of production of NH3 on the NCM electrode reach 5.2% and 0.08 g m-2 h-1, respectively. After functionalization of the NCM with Au nanoparticles (Au NPs) these performance metrics are dramatically enhanced to 22% and 0.36 g m-2 h-1, respectively. These efficiencies and rates for the production of NH3 at room temperature and atmospheric pressure are unprecedented. As this system offers the potential to be scaled to industrial proportions there is a high likelihood it might displace the century old Haber-Bosch process., Comment: 19 pages, 34 figures