I don't know of any easy way to do this. You'd need to build up enough familiarity and experience with a particular sub-field of quantum information research to get a sense of what people are interested in, what has and hasn't already been done, and what you could reasonably work on yourself. By far the best way to do that is to do a research project, PhD, or postdoc in a good QI research group, depending on your education and experience level.
If actually working in a QI research group isn't an option, there are other ways of getting a sense of what's going on in the field, but my suspicion is that they'd require a
lot of patience and self-motivation to see it through:
- Look up some well known research groups or key researchers in QI and look up what they're working on. Group websites and personal homepages may offer lecture notes online. Quite a few QI researchers also maintain their own blogs.
- If you have the time and funds, consider attending schools/workshops/conferences. (The biggest QI conference I know of is QIP, which is held annually, but there are many more.)
- Check the quant-ph section of ArXiv regularly. For this, there's a website called SciRate that I think has a nicer interface. It's also got the advantage that users can log on and "vote" and comment on preprints, which can give you a sense of which work is catching people's eye. (SciRate was originally started by and for the QI community and was extended to cover everything announced on ArXiv not too long ago. There's an option to restrict to just the quant-ph or any other section of ArXiv.)
- If a particular topic gets your attention or interest, try to see if there's a recent review article on the subject.