Yes, it is possible. Your first step would be to learn Quantum mechanics from s standard textbook such as Modern Quantum mechanics: by sakurai, or Principles of Quantum Mechanics: by Shankar. There is nothing such as research in pure quantum mechanics, though there are a small handful of people working on the foundations of quantum mechanics. If you want go to the the physics side of quantum mechanics, you could study Quantum field theory, or condensed matter theory. but it would ve very difficult for you to study these, unless you go through the whole physics undergrad curriculum starting from classical mechanics, statistical mechanics, electromagnetism and a great deal of math. If you want to pursue quantum computing it is not that difficult if you have some knowledge of theoretical computer science. Refer to this question for further information. After reading QM, you may pick up a standard textbook on quantum computing. Many universities will accwept PhD applications in these areas as long as you have the knowledge in these areas, though you should have sufficicient knowledge in Physics to crack exams like the GRE, or JEST, for PhD admissions.