Zetsumetsu Kigu Shoujo: Amazing Twins (2013)

The story takes place in a world where certain individuals possess a power called Incomprehensible Skill of Human beings (ISH), giving them supernatural powers. One of these individuals is Amane Todoroki, a straightforward and somewhat air-headed girl who works as an idol magician for a performance team called Nought. Amane has a twin sister named Lilianne who was born without a body. Unlike Amane, whose ISH is fairly weak, Lilianne is extremely powerful and is able to lend her power to Amane, who uses it in her Nought performances. Amane and Lilianne try to spread the joy of ISH powers via magic shows, but everything changes when Amane is approached by someone from IAM, a group that puts on magic shows like Nought's, but is secretly experimenting with ISH users.