As a fan of the entire .Hack series I beleive that I rate more harsly than the normal person.
NOTE: This review is based on the first 2 OVA's.
Story: Synosspis taken from the Wiki Page: "The story follows the path of three players: Sakuya, Tobias, and Mary, and their playing of the world's largest MMORPG, "The World R:X" created byCyberconnect Corporation. As is the case, these players were on a quest in their party of three, when they are caught in a strange fate of circumstance."
Basicly it is the same story for every .Hack show, but as they say "If it ain't broke, don't fix it." The Story is kinda stale after watching every single .Hack anime, but the change of characters makes for a refreshing story. Another thing was the out-of-place onsen scene, It was un-needed and served no purpose to further the plot other than fanservice of rather plain looking character designs.
Animation: As with most of the .Hack animes, most of the story takes place inside of the MMORPG "THE WORLD". As such the animation is top notch. The only down side is in the second OVA where Sakuya and Tobias' players are traveling to Tokyo. While they are animated in the 2D animation tatic, those walking behind them are animated in CG, The conflicting animation styles did distract me from what was happening, but not enough to make me cut off the anime.
Sound: .Hack has always been superb with the sound, and Quantum is no exception. Although when I watch anime, I don't pay too much attention to the BGM, but what I hear makes me want THE WORLD to be a real MMORPG.
Characters: There is not much to say about the characters, becuase this is a 3 episode OVA series, many of the characters are not devloped enough for many people to make a connection with any of them.
Overall: Great addition to the .Hack series, I highly suggest that you watch this if you are a fan of the .Hack franchise.