This is interesting, where photons that existed at different times can be 
entangled.

https://arxiv.org/pdf/1209.4191.pdf

Entanglement Between Photons that have Never Coexisted 

E. Megidish, A. Halevy, T. Shacham, T. Dvir, L. Dovrat, and H. S. Eisenberg 

Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 
91904, Israel 

The role of the timing and order of quantum measurements is not just a 
fundamental question of quantum mechanics, but also a puzzling one. Any 
part of a quantum system that has finished evolving, can be measured 
immediately or saved for later, without affecting the final results, 
regardless of the continued evolution of the rest of the system. In 
addition, the non-locality of quantum mechanics, as manifested by 
entanglement, does not apply only to particles with spatial separation, but 
also with temporal separation. Here we demonstrate these principles by 
generating and fully characterizing an entangled pair of photons that never 
coexisted. Using entanglement swapping between two temporally separated 
photon pairs we entangle one photon from the first pair with another photon 
from the second pair. The first photon was detected even before the other 
was created. The observed quantum correlations manifest the non-locality of 
quantum mechanics in spacetime. 

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