If all the coins are quantum-mechanical, you should never quit, nor if all the coins are logical (digits of pi). If the first coin is logical ("what laws of physics are true?", in the LHC dilemma), the following coins are quantum, and your utility is linear in squared amplitude of survival, again you should never quit. However, if your utility is logarithmic in squared amplitude (i.e., dying in half of your remaining branches seems equally bad no matter how many branches you have remaining), then you should quit if your first throw comes up heads.