Detection Loophole in Bell experiments: How post-selected local correlations can look non-local

A common problem in Bell type experiments is the well-known detection loophole: if the detection efficiencies are not perfect and if one simply post-selects the conclusive events, one might observe a violation of a Bell inequality, even though a local model could have explained the experimental results. In this paper, we analyze the set of all post-selected correlations that can be explained by a local model, and show that it forms a polytope, larger than the Bell local polytope. We characterize the facets of this post-selected local polytope in the CHSH scenario, where two parties have binary inputs and outcomes. Our approach gives new insights on the detection loophole problem.