Maybe your logic says so, but there is no conflict between QM and SR. Our best theory, QED, combines QM and SR to produce the most accurate predictions we ever had. And QED is the basis of quantum optics, the discipline which performs all these wonderful experiments on entanglement. Nothing wrong there, only somewhat of a no man's land at the very foundation (just as in most disciplines if you dig deep enough).logic says that either QM or SR must be 'slightly' wrong, but at the moment we have no idea which. They are both very solid theories and to my understanding – there must be "a big prize" waiting around the corner for the person(s) who crack this nut...
shows how measurements in a relativistic context are compatible with SR and QM.
There seems to be a conflict between QM and _general_ relativity, but even this is not clear cut.