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fragment describing the gist of the experiment:

"The [entering] microwaves are so far off resonance with the [superconducting] circuit that they cannot drive it between its ground and its excited state. So instead of being absorbed, they leave the box bearing information about the quantum system in the form of a phase shift (the position of the troughs and peaks of the photons’ wavefunctions).

Although there is information about the quantum system in the exiting microwaves, it is only a small amount of information.

“Every time we nudge the system, something different happens,” Murch said. “That’s because the photons we use to measure the quantum system are quantum mechanical as well and exhibit quantum fluctuations. So it takes many of these measurements to distinguish the system’s signal from the quantum fluctuations of the photons probing it.” Or, as physicists put it, these are weak measurements."

What happened to the old idea that when you observe a quantum system, its wavefunction collapses? Is that not true anymore? It seems like these guys observed it "gently" enough that it only sort of mostly collapsed with some bias?
It did collapse, but not before their probe measured something. Then they repeated a million times and averaged the results.
According to the article, what they measured doesn't really sound like a 'real' quantum system: it's a superconducting circuit with two discrete states with an infinite number of previously immeasurable superposition states in between. They call this an 'artificial atom'. Unless I'm mistaken, it's an emulation of sorts.

http://arxiv.org/abs/1202.1923

It is absolutely a real quantum system. It's an artificial atom. It has basically approximately the same Hamiltonian as a trapped atom but at 6 GHz, and we can control the coupling.
It was always a postulate. Now thanks to understanding things like the stochastic master equation better, we understand that wavefunction collapse is a continuous process, and not at all a random one.
Couldn't they use this method to communicate over vast distances? I mean shit you could build a computer that uses something like this to measure the shift in a superimposed particle; this would allow communication to anywhere on earth without physical or wireless connection. All that's need is superimposed particles.
No no no. You can't use superposition to communicate data. Look, if your idea leads to being able to do literally anything faster than light, it's automatically wrong.