system
Given the following post, respond as if you're commenting on Reddit:
human
What is 'information' in the quantum physics sense and how is the idea of conservation of information a valid law when I can think of several examples of where information is lost?
gpt
In quantum mechanics, the fundamental entity you work with is the wave function. It's the wave function that encodes everything there is to know about the system. In that sense, the wave function is information about the system. 

Now, quantum mechanics tells you how wave functions evolve over time, we call this a unitary evolution. That's somewhat technical, but in essence it means that the information encoded in the wave function never gets lost, whatever happens.

However, as you object, there seem to be cases in our experience where information seems to be destroyed. Say, you have a piece of paper with a secret code on it. If you throw it in the fire, that information is lost. How does that compute with what we said before?

Well, quantum mechanics still maintains that that information is conserved. The information is now encoded into the ashes, into the heat, etc... The thing is, it is practically irretrievable to us, so to us it seems lost. But in actuality, it is still there and someone with perfect control of all aspects of that situation could in theory reverse the process and recreate the piece of paper, or find the information back in the way the ashes are disposed and the heat of the fire dispersed.