Biophysics and BME major here, just my $0.02:
Biophysics is an EXTREMELY broad field, basically encompassing all areas of biological research that can be better understood from a physical and chemical point of view (both macro- and micro- scale). Your coursework and research in biophysics should be reflective of your own particular interests, whether it be macromolecular structure and dynamics, neuroscience, imaging, etc. If you want more info on some of the different fields in biophysics just let me know.
To answer your question about taking quantum, again it really depends on your own interests. The only fields in biological and medical research that I know of where a background in quantum would be useful would be imaging and molecular dynamics at the atomic scale. I used to work in a computational chemistry lab that mostly dealt with understanding charge transfer within DNA and proteins, how it helps describe how some proteins functions (likely a very small subset), and a few technology applications (apparently people are using DNA for things like nanowires...) Lots of quantum there. But not particularly many medical applications (I'm assuming since your an MD/PhD applicant you're looking for at least
some translational aspect to your research, or else you'd probably just do a PhD). Can you tell me more about your particular research interests?
As an aside, biophysics has lots of overlap with BME, and lots of strong MD/PhD programs also have strong BME programs (not that many don't have strong biophysics programs as well). From majoring in both, I've found that BME is much more application-based, which probably makes it more easily tailored to an MD/PhD who is interested in more translational research. Whereas biophysics is really more about getting a better understanding of fundamental biological processes, which if you're really interested in basic science would probably be a good route. Then there's medical physics, which is all about imaging, which also overlaps with BME... So I would say if you're interested in "biophysics" I would suggest you also look into some BME or medical physics programs. If you want to see some of the cool things that are going on in these fields, check out the websites of some top university programs and look at what research different professors are doing. Some examples would be for BME: Johns Hopkins, Duke (my ugrad so I can tell you a lot about research here), GaTech, UCSD, Penn, MIT, WashU, UWash. For biophysics, a lot of departments are fairly new, but places like Harvard, Stanford, and MIT are bound to have some really cool research going on.
Hope this helps!