When I flush my upstairs toilet, which is located directly behind the other toilet (which is an identical toilet & works fine), separated only by wall, a large bubble of air erupts from the drain hole of the toilet and then the toilet proceeds to flush very poorly. I have tried dumping a 5 gallon can of water into the toilet and it drains as fast as I can pour into the bowl. However, when I tried flushing the toilet immediately after that I once again got the air bubble. Any help would be appreciated.

Check the vent pipe, you may need a separate one.

I doubt very much that it's your vent pipe. Bubbles indicate a blow back caused by a partial blockage. Let me explain what's happening. You flush the john, The discharge bangs into the partial clog in the line and starts to rebound back pushing a bubble of air ahead of it. That's when you see your bubble. It also impedes the siphon action which gives you a weak flush.
The solution would be to pull the upstairs toilet and snake the drain. Use a new wax seal when you replace the bowl. Good luck.