It's largely about making reads when it comes to keeping Quan down.
Let me see if I can be more specific:
When you knock Quan down, you have a lot of options. If he's doing a delayed wake up, you can actually run him into the corner. Running against a grounded opponent will cause them to be pushed along the ground if they're doing a delayed wake up.
Use a fast jab string, or something with multiple hits. Sky Drop has a lot of start up, so you can armor break him if he tries to use meter fairly easily.
Just because he gets a MB Sky Drop off, doesn't mean he's out of the woods, yet. You can do almost anything to Quan as he's coming down from a Sky Drop
Njp, throws, uppercuts, strings all work on Sky Drop on the way down.
Quan Chi players use and abuse his exceptional NJP, so you need to keep an eye out for it. Your best bet is to bait it and try to trip guard him on the way down.
I hope this helps.