Violation of Bell Inequalities with a Mixture of Separable States in a Multiple-Photon Absorption Attack on Ekert Protocol

We propose a new type of attack on Ekert protocol in which, rather surprisingly, Eve drives a violation of Bell inequalities in Alice's and Bob's detectors with a mixture of separable states. She does so by sending correlated pulses containing several photons at frequencies where only multiple-photon absorptions are possible in their detectors. Whenever the photons stemming from a same pulse are dispatched in such a way that the number of photons is insufficient to trigger a multiple-photon absorption in either channel, the pulse remains undetected. We show that this simple feature leads to violations of Bell inequalities that can match closely those predicted for entangled states, even in the simplest cases of two-photon and three-photon absorptions.