I have to say pretty good.
I assume it was very hard to make an Anime such as this and actually keep the audience hooked considering the core story requires you to know things about Quantum Physics.
This provides a better explanation than anything I might've garbled up:
Premise is pretty simple, it's really the moral point of the story that drives this thing home. I didn't quite like that it was so overstated they actually had one of the characters speak it themselves near the end, but I guess for an anime that gets tangled up quite a bit through the middle, they needed to set the record straight in the end so there'd be no confusion as to the message they were trying to get across.Noein features the concept of time as a dimension which resonates with other time spaces. The symbol of the Haruka's Dragon Collar (竜のトルク) is an Ouroboros.
Noein thrives exceptionally in the many theories of quantum physics. Particularly, it puts forth the concept of Everett's Many-Worlds Interpretation (MWI), which is seen that the universe is branching off into a series of infinite probabilities.
However, Noein also includes the theory of the Copenhagen Interpretation, which suggested that an observer/measurement is important to determine the decoherency of the probability. In the anime, Haruka, the lead character, has the power of "observer-status" in the multiverse, thus enabling her to determine the outcome of an event just by "looking" at the event itself.
Also, in one episode, Uchida candidly explained to her bodyguard Kooriyama about the Schrodinger's Cat, whereby the observer only determines the death of the cat when he/she opens the box. She also mentioned the famous phrase "God does not play dice", as quoted from Albert Einstein.
While the Many-Worlds Interpretation suggested the idea of a diverging time-space, the anime also featured a probability where a converging time-space occurs, as has been deliberately induced by the main antagonist, Noein.
The art department seemed to have had its funding cut somewhere around the 17th episode which resulted in the "good" animation being only presented where absolutely necessary, while some of the scenes would've looked better if I drew them myself. But I can't really blame them for it, considering it was probably a logical move as they neared the end.
Coming back to the story, I have to say, it's some contemporary good zen shit. The Quantum Mechanics theories they've incorporated and executed into the thing worked nicely after I had some basic wikipedia reading sessions to figure out what the hell they were talking about. If you want to watch this, you will really need to know what Alpha, Beta and Gamma rays, Everett's Many-Worlds Interpretation, Copenhagen Interpertation (as seen above), and so on as they're mentioned throughout the anime.
All in all, if this is the sort of stuff that interests you (and you'll note, there isn't a lot of entertainment out there incorporating these elements) then it's really a treat I'd say.
Pretty good in my opinion, really reccomeneded for anyone - this kind of stuff should be basic knowledge and it's a shame the entertainment industry doesn't explore this aspect of our reality as much as some others.
To reiterate - reccomended.