When I camp away from a water source, I figure 2.5 liters to get me through dinner, breakfast, and some water to start the day. That has always worked well in the past. Also, one one trip I recall, I ate dinner, watered up with 3 liters, and hiked a little ways to a campsite; then in the morning, went until noon before reaching a water source. I had drunk all my water and was pretty thirsty by the time I reached that water.
For the hike up, let's say it will take you 4 hours. I'd drink up before starting to hike and I'd figure 2 liters to drink along the way. You'll come down pretty fast in the morning, so as long as you have water at the car you'd be fine with what's left over from the camp allowance. So that puts us at 4.5 liters. That's what I'd take. And I'd drink extra water the day before the hike to ensure that I was well hydrated before starting.
My numbers assume dehydrated food, so f you are carrying food that does not require rehydrating, you would not need quite as much water.