Does the wave function collapse cause information to be created? If I understand correctly, a principle of physics is that information is never created or destroyed. And, unless information is defined differently in physics, according to information theory there is information whenever an event, out of more than one possible events, occurs. The typical example is a coin flip, which would contain 1 bit of information because there are two possible events and one of them occurs, so we obtain information when we learn which of these possible outcomes actually occurred.
I understand that in a deterministic world, coin flips only seem to be probabilistic, but in reality, the probability of being heads or tails was already determined, so one of them really had a probability of 1 and the other had a probability of 0. So there was really no new information here; the information of whether it'd land heads or tails was already contained in the state of the system around the coin and we could've predicted the outcome if we knew enough about the coin's surroundings.
But in quantum physics, unless I'm dead wrong on my understanding of QM, the wave function collapse is pretty much an actual random coin flip. So then wouldn't running a quantum experiment and observing the result create new information?
 A: great question, I believe you are really asking if QM and its wave function, which shows the probability distribution is really random, or is there something in the microcosm that we do not understand and we handle it random, but it is really just that we do not have enough information about the system that builds up the microcosm, so we do not know how to calculate the outcome.
As per QM, the wavefunction of a particle is the probability distribution of the particle really in space. You have to make many measurements, to get the map of the outcomes. The example is the double slit experiment, where you really get to see the probability distribution as a map on the screen.
QM describes the outcomes with the wavefunction. If you make one measurement, it is random, which distribution you will get from the map. But if you make enough measurements, you will see the pattern.
Your question is really why QM does do it randomly. It is because although QM gives the best mathematical description for the outcome of the experiments about the microcosm, we still do not know exactly what is going on in the microcosm in classical (layman) terms. We do not know exactly if particles are really pointlike (they are pointlike in the current accepted views, but string theory gives another explanation) or what it means that an electron has rest mass but no spacial extension. We do not know what a quark really is, or what it looks like at the planck scale. We do not know why the Pauli principle really goes for one type of particle but not the other and how that looks in a classical view or our common sense.
Things just work differently at that size and QM still gives the best description. Our energy levels in our experiments do not allow us to check what goes on at Planck scale.
A: Your question can be resolved through understanding some terms better.
A coin flip does not 'contain information.' A coin flip is a stochastic process that generates a random outcome. A well-defined stochastic process is associated with a probability distribution that has a well-defined associated information-entropy. For the toss of a fair-coin, this is one bit.
When you measure the result of a coin-toss, you gain information about the state of the coin. If your previous information was, "The coin's value is determined by a coin toss," and your new information is, "Heads," your information about the coin's state has increased by 1 bit. This will be exactly the same as measuring the difference in entropy for your prior and posterior distributions.
Now that we have that background, we can really talk about information in fundamental physics. While a coin-flip, as we have considered it is a stochastic process, it is also a deterministic process. That is, if we took an accounting of the exact dynamics of the flip and the exact initial state of the coin before the toss, we could calculate (supposing we had enough computational power) the final state of the coin perfectly and we will have gained no information about the coins state from measuring it.
In fundamental physics, it is possible to treat ANY physical process in this way, as the dynamical evolution of some closed system. Hence the principle that 'information is never destroyed'. This is just (sloppy?) shorthand for: Any state is recoverable as long as we perfectly understand the exact state and dynamics of some large enough system (where large enough system might be the entire universe) and have unlimited computational power.
Hopefully this is enough to understand why it's strange to say that measurement collapse 'creates information.' Information is a property of a description (in our case a probability distribution over state). When we measure something (quantum mechanically or no), we are increasing the accuracy of our description.
You might wonder if wave-function collapse destroys information. If you understand paragraph 4 you will see that it does not. The trick is that the information is stored in some larger system, one that includes the quantum object and you the measurement-taker. Some exterior being could in principle reverse this larger system and somehow recover the original state of the quantum system. There are a lot of problems with this- quantum states cannot be measured to unlimited accuracy or reversed as easily as classical states, and again you would need nearly unlimited computational resources.
A: Wavefunction collapse doesn't actually exist. It's only a feature of the Copenhagen interpretation of quantum mechanics. If it did exist, it would be destroying information, not creating it, since collapse is represented by a projection operator.
A: Wave function collapse is just an interpretation. No information created when you roll a dice and it turns out be a 6.
