It's called Minamitorishima, and it's a small atoll in the Pacific Ocean. It is one of the most remote islands in Japan's vast archipelago, so much so that it lies nearly 2,000 kilometers southeast of Tokyo. Yet from the depths of the surrounding seas may come a tremendous gift for the country's economy. It is there, as deep as 6,000 meters undersea, that a group of Japanese researchers succeeded in a veritable mission impossible: the recovery of sediments containing rare-earth elements from one of the most promising underwater deposits discovered in recent years. The feat is set to strengthen Japan's role in the increasingly crucial rare earths sector, a central element in the trade war between China and the United States . Indeed, Japan is the only major industrial country that, while remaining partially exposed, has managed to significantly reduce its dependence on Beijing.…