Magic trick with two scrambled Rubik's cubes

Showing a magic trick which can be performed with two Rubik's cubes. The cubes are differently scrambled, and you then ask someone to scramble the cubes further, using as many moves as they wish, and without showing you what they are doing. The only condition is that they perform the same sequence of moves on both cubes, so if they turn the face with the white center sticker 90 degrees clockwise on one of the cubes, they must also turn the (differently looking) face with the white center sticker on the other cube 90 degrees clockwise and so on. When they are done, they may hand you any of the two scrambled cubes, and you'll bring it into the exact same state as the other scrambled cube without even looking at any of the cubes. There is no cheating involved, just pure mathemagics. :)