**Mladen Pavicic**

*Max-Planck-AG Nichtklassische Strahlung,
Humboldt University of Berlin, D-12484 Berlin, Germany.
*

*Department of Mathematics, University of Zagreb,
GF, Kaciceva 26, POB-217, HR-10001 Zagreb, Croatia; mpavicic@faust.irb.hr; http://m3k.grad.hr/pavicic
*

** Abstract. **
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.

**PACS numbers: **42.50.Dv, 03.65.Bz.

**Keywords: **four photon interferometry, non-maximal singlet
entaglement, quantum optics,
quantum nonlocality, loophole-free Bell experiment, Hardy's
inequality.