"What persons may and may not do to one another limits what they may do through the apparatus of a state, or to do to establish such an apparatus."
Perfect. It's succinct, crystal-clear, and altogether principled. Indeed, it's virtually the whole of libertarianism in a single sentence--so much so that I doubt if many non-libertarians would ever agree with it. To my non-libertarian readers: Do you accept Nozick's claim? Or do you find that agents of the state may do more than ordinary individuals acting in the state of nature?
It isn't clear to me what Nozick is claiming here. Well, presumably he begins with a notion of natural rights, understood as side-constraints on the actions permissible for an individual, and then claims that the state must likewise respect these rights. But this argument doesn't even get off the ground for those of us who share Bentham's suspicion that natural rights are "nonsense on stilts".
So let us instead take a broader interpretation, where we are simply concerned with what is morally permissible (as determined by the true moral theory: some form of consequentialism). His claim no longer makes much sense. It is either trivially true, or patently false. For once we reject absolutism, the question of "what persons may and may not do to one another" will be influenced by situational factors (e.g. what the consequences of performing a particular action would be). And if one is acting through the apparatus of the state, then one is in a different situation than one would be in the state of nature.
Now, this factor will influence what it is morally permissible for the person in that situation to do. The "all things considered" conclusion yielded by our moral theory will take this factor into account. On this interpretation, Nozick's claim is trivially true: of course what government agents may do is going to be limited by what they may do. It's tautological.
Alternatively, the claim might be that what individuals may do in different situations limits what they may do in this situation. And this claim, if we reject absolutism, is quite obviously false. The right thing to do will depend, in part, on your situation and circumstances. You cannot say in advance that the limits appropriate in some situation can generalize to all others. That's absolutism, which - as has already been said - we reject.
So, speaking as one of Jason's "non-libertarian readers", my reply is that Nozick's claim doesn't make any sense once divorced from his absolutist libertarian framework. Nor does it make sense to ask whether we non-absolutists "accept" it. I'd accept the trivially-true reading, of course, and reject the trivially-false one. But either way, it's trivial.
P.S. I use the term "absolutism" to refer to the view that moral facts are determined by act types and are not sensitive to situational factors such as what the consequences of a particular act would be. For example, Kant was an absolutist, holding that lying was always wrong, no matter the circumstances. Constraining Rights theorists are absolutists in that they hold that violating a right is always wrong, no matter the circumstances. The opposite of absolutism is not "relativism", but simply taking circumstances into account, as in consequentialism. The utilitarian, for example, can hold that a particular action is "objectively wrong", though it might have been right in different circumstances, if that would have maximized happiness or human well-being.