The Third: The Girl with the Blue Eye
From OtakuWiki
Synopsis
It was a long time since the Earth was devastated by a great war. Much of the planet was reduced to an inhospitable desert inhabited by giant insects. The planet is monitored and guarded by an mysterious alien race known as "The Third"... named for the single red astral eye on their foreheads, which enable them to control machinery and computers. They also strictly regulate how much technology Earth is allowed and how much they can progress, and the punishments can be very severe - sometimes but not always deadly.
Honaka, a.k.a. "The Sword Dancer", is a 17 year-old girl that travels this desert. A “Jack-of-all-trades” who is also very talented with a katana. She, along with her sand tank's A.I. Bogie, take on all manners of jobs from minor repairs to fighting the giant insects... just as long as one of them doesn't include taking human life. But as strange as it seems, the very-human Honaka is also a Third – but her astral eye is blue and doesn't have the same abilities as the others – but it does help her to perceive danger, as well as delivering a powerful psionic attack to opponents.
Lately though, Honaka had picked up a stranger wandering in the desert – a handsome young-looking man known as Iks – one which the rest of the Third are interested in. Honoka is also stalked by one of the Third's Techno enforcers, a heartless mecha known as Blue Breaker - who had killed a tech friend of hers and made his young daughter an orphan - which could test her in ways she may not be able to keep up. And there's always Joganki, a Third who is intrested in Honaka and watching out for her - but for what, he's not telling.

