Since you are studying Physics, may I introduce you to this little book, whcih will answer all your questions and more.
When working with a subject, even one I know well, I like to keep two (sorts of) books on the subject.
A very basic book that explains things, including the maths, but is not too big and encyclopaedic.
A treatise type book that works out all the special cases, wrinkles and details for when I need to delve deeply at a particular part of the subject.
Susskind has written 3 titles covering much of Physics using of the first type of book and this is the one you need.
It contains the whys and wherefores of quantum calculations, including useful tables of results, for entanglement, density matrices and compares with classical analogues, discussing the difference between quantum and classical versions.