Pour the pomegranate juice, vodka, pomegranate arils, and simple syrup into a large pitcher. Stir well to combine.
Just before serving, add the prosecco and ginger ale. Stir gently to combine. You can add ice to the pitcher or to the serving glasses before pouring the punch.
Notes
If you're using asti instead of prosecco you may not need as much simple syrup as asti is sweeter than prosecco. Start by using 1 tablespoon of simple syrup. Then, when you add the sparkling wine, adjust the sweetness of the punch by adding more simple syrup if desired.