Dear aspirant, 

Hope you are doing well. As per your query yes you can do masters in quantum physics in which quantam mechanics is a part after doing BSc in physics but as you mentioned that you are in bio stream so I should inform you that you have to have maths as a subject in your+2. Hope you find this helpful. Thank you. 

Hello...

In one word I will say yes you can. See there is no any basic rules that people don't having math streak can't study quantum mechanics further.

Only one thing is that if person is from science stream in 12th and read physics in graduation then he or she is qualified for further education of quantum mechanics .

For further queries feel free to comment.