The Third: Aoi Hitomi no Shoujo [TV]

In the distant future, because of an interplanetary war that has continued on for centuries, the civilizations were ruined. Human beings have lost everything, and only 1/5th of the population survived. Pseudo-humans, The Third, are said to have appeared just after the war. They have a third red astral Eye on there forehead. Hence the third. Using them, they can control computer systems and so on, and rule the world by their superior intellect and abnormal abilities.

In this dark world, there is a girl named Honoka. She is a master-of-all-trades, and she accepts any job except taking a human life. She is also a master of chi and swordsmanship and is known by most as the Sword Dancer.