Reading about the concept of 'information' in physics, I have often read the Shannon definition of information contents, i.e. how compressible the description of something is. A truly random number can not be expressed in any shorter way than itself, thus having a high information contents, while other seemingly very complex phenomena can be compressed to some initial conditions plus a simple algorithm, therefore having a small information contents. But in quantum physics, those algorithms (the equations dictating the evolution of the system in time) do not have fixed outcomes, they are only probabilistic. The same initial conditions and the same equations can lead to completely different outcomes. Then I wonder how can the information contents be attributed. It looks like knowing the initial conditions and knowing the algorithm(s) is no use, we still have no idea what the outcome will be. A significant portion of the required information for determining the final state comes from 'chance' and is therefore forever hidden from us. Conversely, it seems that some particular physical situation can (in principle) have been the outcome of different initial conditions and different algorithms, just affected by different outcomes of chance. So it seems that in the quantum realm, a physical situation can never be compressed to initial conditions plus algorithm. Chance always plays a role in the output, so the Shannon concept of compressibility breaks down, nothing should be compressible because we can never know the contribution of chance to the outcome. Where am I wrong?