Based on conversion:
1 liter of milk is equivalent to 1.05669 US liquid quart. (1000mL)
While 1 quart of milk is equivalent to 0.946353 liters. (946.353mL)
This concluded that a liter would hold more milk by 0.053647
liters or 53.647 mL.
But if you are talking about an imperial quart, this will hold more milk than a liter. Because its measures 1136 mL which is 136mL bigger than the liter.