It seems like all the time bending in Quantum Break requires some harddrive space. The official Xbox Store accidently revealed the full file size earlier today and WCCFTech was quick to save the evidence before Microsoft removed it. A whopping 44.09 GB of free space is required for Xbox One, and the PC version is likely something similar since it usually doesn't differ much between formats.
So be sure to make some space if you're drive is full. We recently got to play the game and believe us when we say Quantum Break is something you don't want to miss.