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We investigate dynamical generation of macroscopic nonlocal entanglements between two remote massive magnon–superconducting-circuit hybrid systems. Two fiber-coupled microwave cavities are employed to serve as an interaction channel connecting two sets of macroscopic hybrid units, each containing a magnon (hosted by an yttrium–iron–garnet sphere) and a superconducting-circuit qubit. Surprisingly, it is found that stronger coupling does not necessarily mean faster entanglement generation. The proposed hybrid system allows the existence of an optimal fiber coupling strength that requires the shortest amount of time to generate a systematic maximal entanglement. Our theoretical results are shown to be within the scope of specific parameters that can be achieved with current technology. The noise effects on the implementation of systems are also treated in a general environment, suggesting the robustness of entanglement generation. Our discrete-variable qubit-like entanglement theory of magnons may lead to direct applications in various quantum information tasks.

Brain networks extracted by independent component analysis (ICA) from magnitude‐only fMRI data are usually denoised using various amplitude‐based thresholds. By contrast, spatial source phase (SSP) or the phase information of ICA brain networks extracted from complex‐valued fMRI data, has provided a simple yet effective way to perform the denoising using a fixed phase change. In this work, we extend the approach to magnitude‐only fMRI data to avoid testing various amplitude thresholds for denoising magnitude maps extracted by ICA, as most studies do not save the complex‐valued data. The main idea is to generate a mathematical SSP map for a magnitude map using a mapping framework, and the mapping framework is built using complex‐valued fMRI data with a known SSP map. Here we leverage the fact that the phase map derived from phase fMRI data has similar phase information to the SSP map. After verifying the use of the magnitude data of complex‐valued fMRI, this framework is generalized to work with magnitude‐only data, allowing use of our approach even without the availability of the corresponding phase fMRI datasets. We test the proposed method using both simulated and experimental fMRI data including complex‐valued data from University of New Mexico and magnitude‐only data from Human Connectome Project. The results provide evidence that the mathematical SSP denoising with a fixed phase change is effective for denoising spatial maps from magnitude‐only fMRI data in terms of retaining more BOLD‐related activity and fewer unwanted voxels, compared with amplitude‐based thresholding. The proposed method provides a unified and efficient SSP approach to denoise ICA brain networks in fMRI data.