PhD in Quantum information science/ quantum physics without intensive formal education My undergraduate degree is in B.E electronics and electrical engineering. My undergraduate gpa is kind of pathetic because I was never interested in engineering but rather B.S physics. Unfortunately I was forced into engineering. Later I went on to pursue M.S in nanoscience with really good gpa. Except that it was not focused on quantum dynamics or quantum physics intensively. I had a course of nanophysics but it covered only fundamentals ( the textbook used was ' introduction to quantum mechanics ' by Griffiths ). That's about the maximum quantum physics I could get from my MS since there was no applied physics department in my institute, only nanobiophysics. I have 2 papers published as conference proceedings and a poster presentation but not related to quantum theory.  Nevertheless I did not give up hope. I am really trying hard to get a PhD position in Quantum physics/ condensed matter physics/ quantum information science. I am pretty much an autodidact I.e I self educated myself in advanced quantum physics by going through books like ' quantum computing and quantum information science ' by Nielson and Chuang. Also learning through open source lectures from professors like Dr. Sergey Frolov in Quantum Transport and Dr. Leonard susskind in Quantum theory/ quantum mechanics/ quantum entanglement.

I somehow don't want to apply within the US because I am more attracted to the European research philosophy or the research carried out in Asian countries like Singapore or even Australia. The problem I face is that professors think I don't have the sufficient formal education in the field which is true. Professors reject my requests just because of this. I consider myself to be extremely motivated and determined to pursue a PhD in Quantum physics with a goal to get into academia. My motivation is not monetory but more of intellectual pursuits and curiosity to learn. I have also offered professors that I will work during my PhD without a stipend. It is a dream I'm fighting for and am willing to go to any lengths to achieve my goals. Lately, I have been feeling scared and taking blows to my self esteem due to the rejections. Self doubt is creeping in where I have begun questioning my intellectual prowess. But I'm still trying hard to learn on my own and carrying out research as an independent scholar staying up for days and nights straight. 

I feel lost and am not sure what do I do next. Hoping to get responses from veterans and achievers In the field.
If the professors you have spoken to (who presumably know you better than we do) believe you need more formal education in the field to be successful, you should pursue more formal education in the field (such as a masters.) 


  I consider myself to be extremely motivated and determined to pursue a PhD in Quantum physics with a goal to get into academia. 


If you really want to do quantum physics and you're told that you need some formal background to be taken seriously as a PhD applicant, then get that background.  

Given that you are, in fact, passionate about doing quantum physics, you should presumably even enjoy that masters, especially if it is a research-based program and not just taught coursework. 


  I somehow don't want to apply within the US because I am more attracted to the European research philosophy or the research carried out in Asian countries like Singapore or even Australia. 


In many places in Europe, a master's degree in the field is a requirement for starting a PhD. In the US, however, many PhD programs do not expect prospective students to have a master's. So if you're really set on not getting another master's, you should strongly reconsider this attitude.

You wrote in a comment:


  Let's say I do go for masters. Spend a huge sum of money from my parents pocket or perhaps take a loan. So then I would have three degrees. What's the point. Is there any respect for people who have spent so much time, devoted their years to science. What respect do people have for intellectuals unless you are an Einstein or Feynman; what I mean is unless you are from some top notch university who's going to notice you.


I don't know what "respect" has to do with anything. There is no number of degrees that is sufficient to guarantee that people will "respect" you. 

If you, personally, would find it extremely distressing to devote years - decades, even - to science and still not be respected as an Einstein or Feynman, then you should probably look for another career. 
A significant portion of people who seek to become professional scientists do not succeed in this goal. Of the ones who do succeed, the vast majority never reach the level of influence of Einstein or Feynman. If the overwhelming probability that you will not become a "famous" scientist makes this path seem less appealing, you should probably find another. 

("A man must love the thing very much if he not only practices it without any hope of fame or money, but even practices it without any hope of doing it well." --G.K. Chesterton)