# Can entanglement swapping be performed on already-entangled photons, and if so, can it preserve this entanglement over the swap?

Consider 2 uncorrelated photon pairs (a1,a2), (b1,b2) such that (a1,a2) are entangled, and separately (b1,b2) are entangled. We wish to entangle-swap so as to end up with a new entanglement (a1,b1) by using the ancillary photon pair (a3,b3), such that (a1,a3) are entangled and (b1,b3) are entangled. This suggests that we do a multipartite (3-way in this case) entanglement preparation prior to the swap, such that (a1,a2,a3) are entangled, and separately (b1,b2,b3) are entangled.

The swap proceeds in the usual way by Bell state measurement on a3 and b3, and we end up having entangled (a1,b1).

The question is whether, after this operation, the entanglements (a1,a2) and (b1,b2) remain intact? If not, can we modify the procedure to guarantee this? If yes, will (a2,b2) now be entangled as a result of the swap? (they were uncorrelated before it). If not, how can we arrange that they are entangled, by only manipulating the other 4 photons?

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