That's not quite the right analogy -- it misses the point a bit. In that analogy the two numbers have definite values right from the start -- they're just ordinary boxes with ordinary numbers written in them. In a more quantum mechanical analogy, the numbers inside the boxes would be undetermined until the observation was made, and yet you would always find that the boxes had the same number inside, even if they were opened simultaneously and many light years away from each other.

Under the Copenhagen interpretation of quantum mechanics, there is in fact some kind of spooky "instantaneous" communication going on between the particles -- one of them needs to tell the other "oh no, my wavefunction has just collapsed in such-and-such a basis and your value now has to be |X>".

Complicating this even further is the fact that relativity tells us there's no such thing as "simultaneity" when we're talking about things happening at different points in space, and so while it looks to one observer like the faster-than-light signal must have gone from Ted's box to Bob's box, to an observer moving relative to the first observer it might look like the faster-than-light signal actually went from Bob's to Ted's.

Some other interpetations of quantum mechanics (in particular, no-collapse aka "many worlds" interpretations) this faster-than-light signalling doesn't occur... though these interpretations have other counter-intuitive features instead.

Even if there _is_ faster-than-light signalling between particles, though, you still can't use this to send a message, because the information you get is always just a random string of bits -- there's no way to actually send useful information.