I am an electrical engineer that just graduated, and I would like to know more about what's being done nowadays in the Information Theory area, as I am interested a lot in it and maybe I will start a PhD.
As far as I know, Information Theory has been used until now for data compression and communications, and multiple results have been obtained for both of them as Shannon's capacity theorem or capacity calculations for some specific channels as the AWGN channels and more.
However, I am not sure which path has this beautiful science taken, and I would like to know which areas of nowadays are making an extent use it, or need it. Apart from it, I would also like to know some problems in the theory that remain unsolved (as the deletion channels, see: https://en.wikipedia.org/wiki/Deletion_channel).
Seems that Quantum Information theory is being widely studied nowadays, so it is also interesting for me to know which is the trend there nowadays, and if a deep understanding of QM would be necessary to study that field.
I have also been reading that the concepts of the classical information theory change in the quantum approach (example, Von Neumann entropy: https://en.wikipedia.org/wiki/Von_Neumann_entropy). References or information to tohose will also be helpful.
I will receive happy any Information about those topics so as can be references, books or just a mention about what's being done. Thanks in advance.