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I'm doing research to interpret quantum physics in terms of the concept "matter is information". I'm trying to understand what is information.
I like the explanation in https://physics.stackexchange.com/q/2689 (including what is commented by Noldorin and Anixx). Could someone suggest me the book/papers which expand that? I seek both the mathematics and the intuition behind.
I have skimmed a couple of quantum information books. They seem to be useless overkill for the moment.
It is worth noting that the term information is used in several different ways: there is no single true definition.
Obviously Information Theory books talks about one version, stemming from Shannon Information. It can be combined with statistical mechanics and statistical inference (Jaynes1, Jaynes2).
How the entropy in information theory is related to the entropy in thermodynamics is a rich and big topic.
Whether information is physical is another big topic; see Aaronson for a good argument and references.
You are likely looking more for John Wheeler's "It from bit" concept of physics. There is digital physics, but it contains a lot of disparate approaches, from Wheeler's fairly philosophical perspective to assuming the universe is a computer or is run on one.