Complete Correlation, Detection loophole and Bell's Theorem
  Two new formulations of Bell's theorem are given here. First, we consider a definite set of two entangled photons with only two polarization directions, for which Bell's locality assumption is violated for the case of perfect correlation. Then, using a different approach, we prove an efficient Bell-type inequality which is violated by some quantum mechanical predictions, independent of the efficiency factors. 
Afshin Shafiee and Mehdi Golshani