I assume that thinking about battery capacity form first principles, the theoretical limit is reached when the charged battery consists of 50% matter and 50% antimatter, right?
Then during discharge, the reaction between the two would turn the matter/antimatter into energy.
How would that stack up against the 500Wh/kg stated here?
Update:
Did a bit of googling (Note to my future self: AI was still bad at math in 2023): Looks like 1kg of mass cointains about 25x10^9 Wh.
So if the above assumptions are right, we still have 8 orders of magnitude to go. An electric car with an optimal battery could go 100,000,000 times further on a single charge than the current ones.