Every year, I lead a group on our annual one-day hike of Whitney. My recommendation is to carry three quarts of water and a water filter. As has been pointed out here, a water filter weighs less than a quart of water. There are many reliable sources of water along the trail to filter as needed; Outpost Camp at 3.5 miles, Mirror Lake at 4 miles, Trailside Meadows at 5 miles, and Trail Camp at 6 miles. You also should have a spring available roughly between switchbacks 15 and 23, but do not always count on this. Remember, once you leave Trail Camp, it is 10 miles roundtrip back to Trail Camp.
Whitney Mike