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AI is a normal practice in the field of medicine. Neural data applications in brain-related AI systems such as neural computer interfaces and the analysis of brain diseases have neural data as input. This kind of information is rather personal and confidential. Because of this, the issue of privacy and information safety is of high priority. The federated learning will help reduce such risks as training of AI models in many different devices or hospitals and it does not involve the flow of raw patient information. Although this solution has improved the privacy, there remain several problems with the traditional federated learning. They include the high costs of communication, lack of privacy protection, and failure to process deep and uneven brain data. Quantum machine learning offers to some extent help in overcoming these challenges. Quantum tensors Networks can code complex data using fewer parameters. This will improve learning efficiency. When quantum tensor networks are deployed, quantum-enhanced federated learning can be utilized in order to deliver more secure and privacy-conscious neuro-AI systems. The combination of these approaches in the healthcare practices is discussed only superficially in this review. It outlines the central ideas, system architecture and privacy. Other topical issues, such as the insufficiency of quantum equipment and the impossibility to transfer the developed practice to practice, are also covered in the review. Overall, one can observe that this paper will help the researchers to understand this emerging discipline and support further study of the subject of safe and confidential neuro-AI systems.