I noticed people were looking for Absolite on here. I've seen quite a few posts about finding it postgame, but not where exactly.
After you beat the game, you'll go to Lumiose City & Sycamore will tell you to use the train to the Lumoise Station to go to Kiloude City. When you get there go to the last set of steps you see before you hit the barrier & go up those steps, go up the other set of steps right after & make a left & go up the stairs right after that & you'll see Serena. Battle her & she'll give it to you.
I read somewhere you needed to battle around 8 times in the battle mansion first.
I did 4 or 5 times before "interrupting" my streak, ie. take a rest, and when I went outside Serena was there and ready to battle. I'm gonna go ahead and say you need to have received BP at least once to unlock it.