One of the themes of current scientific progress is getting more and more information out of tiny amounts of data.

I think that if the universe was once a single spot and everything we see comes from there, then the information about everything is everywhere. If we had knowledge of the mechanics and enough computing power we could understand what has happened in the universe since the start just by observing the current state of one atom.

This is because, if we could measure them with full precision, the current position, direction, and speed of an atom (and all other measurements if we could do them physically) are only possible with one and only one specific history of everything else in the universe.

...to what extent can people be re-created from what they've left behind them...

I think us or any other intelligent species that continues after us will control every aspect of our environments. Just like now we are starting to understand the full "language" of DNA and we are in the first steps of cloning, AI, etc., we will also control the planetary weather, solar system level direction and orbits of planets, etc.

In this context it will be very easy to replicate past living beings. The problem is that because they will be operating on a different set of materials (h2o, salts, carbon, etc.) it will not actually be that original person even if it's an exact replica.

Unless there is some sort of entanglement possible, I think that If a person is copied, the copy is not the original person unfortunately, so when we die we will not be back unless its on the same set of materials, which is possible, but very improbable.

EDIT: The above phrase:

This is because, if we could measure them with full precision, the current position, direction, and speed of an atom (and all other measurements if we could do them physically) are only possible with one and only one specific history of everything else in the universe.

Replaced the original sentence:

This is because the current position, direction, and speed of an atom (and all other measurements that can be done physically) are only possible with one and only one specific history of everything else in the universe.

To reflect, as observed in the comments below by lesswrong.com/user/asr/, that "You can measure those things to only finite precision".