= Photonic entanglement-swapping experiment
In 1998, <Jian-Wei Pan>, <Dik Bouwmeester>, <Harald Weinfurter> and <Anton Zeilinger> created two <photon> pairs by two passages of a pulsed pump through a <crystal> using <spontaneous parametric down-conversion>. Interfering the inner <photons> at a <nonpolarizing beam splitter> implemented a partial <Bell-basis measurement>. Narrow <optical filters> and spatial filtering removed distinguishing information; changing the outer <polarizer> bases checked the conditional correlations. Fourfold detections selected the <entanglement swapping> events. The reported interference supported conditional <quantum entanglement>, but the paper reserved a statistically significant <Bell inequality> violation for improved visibility; it was not a demonstration closing the <detection loophole>.<Experimental Entanglement Swapping: Entangling Photons That Never Interacted by Jian-Wei Pan and others>[pp. 3892-3894, Eq. (3), Figs. 2-3; visibility discussion]{ref}
The ideal calculation makes the distinction between conditional and unconditional <quantum states> explicit. Start with <spin singlet states> $|\psi^-\rangle_{12}|\psi^-\rangle_{34}$, where $|\psi^-\rangle=(|HV\rangle-|VH\rangle)/\sqrt2$ and $H,V$ denote orthogonal <photon polarizations>. Taking the <inner product> with $\langle\psi^-|_{23}$ gives $-|\psi^-\rangle_{14}/2$: expanding the four terms leaves precisely the two antisymmetric outer terms. That <Bell-basis measurement> outcome has <probability> $1/4$ and leaves the outer pair in a <spin singlet state>. Ignoring the inner outcome instead leaves the outer <density matrix> $I_4/4$, a <maximally mixed state>. A conditional preparation flag is useful for later <Bell tests> only with the timing and setting conditions in <setting-independent heralding preserves Bell locality>.
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