Pour the pomegranate juice into a small pot and set over medium-low heat.
Cook until the juice has reduced to 1/4 cup and is thick and syrupy, roughly 20 minutes.
Set aside to cool.
In a small mixing bowl or mason jar, combine the cooled pomegranate syrup, champagne and balsamic vinegars, and olive and canola oils; season lightly with salt and pepper.