In Avengers: Endgame, how does past Nebula have access to the memories of Nebula in the future timeline?
Some sort of quantum entanglement I guess. There is a paradox in physics called the EPR (Einstein-Podolsky-Rosen). It is like spins of particles and stuff. I'm not going into details because my knowledge here is limited.
But, that is the idea in Avengers: Endgame. Because essentially, Nebula is an alien artifical intelligence and so her "components" possibly semiconductors behave exactly like quantum physics "tells" it to. Of course, all these possibilities are only possibilities. They need not even be so - since quantum physics as we know it is probabilistic in its current understanding.
I don't recall the exact wording but there are TWO Nebulas (Past Nebula & Present Nebula) in 2014 (when Present Nebula travels back in time).
They share a common (quantum?) "network" in 2014 (I think that was the term) so Past Nebula has access to Present Nebula's memories and can display them to Thanos.
Think "Galactic Wifi"...they can share data because they are on the same network and frequency but only when they are both in the same time.
Large portions of Nebula have been replaced with cybernetics. It's not really that the two Nebulas "share" this cybernetic neural network - it's that the two cybernetic neural networks are identical, but one is older. Present Nebula wasn't aware that going to the past would result in this security breach presumably because Thanos would have been the one fully aware of the changes he had made to her.
The presence of two Nebulas within the same time period results in both Nebulas picking up interference off each other.