A method for reaching detection efficiencies necessary for optical loophole-free Bell experiments

A method for preparing a loophole-free four-photon Bell experiments which requires a detection efficiency of 67% is proposed. It enables realistic detection efficiencies of 75% at a visibility of 85%. Two type-II crystals each down convert one correlated photon pair and we entangle one photon from one pair with one photon from the other pair on a highly transparent beam splitter. The entanglement selects two other conjugate photons into a Bell state. Wide solid angles for the conjugate photons then enable us to collect close to 100% of them. The cases when both photon pairs come from only one of the two crystals are successfully taken into account. Hardy's equalities are discussed.