Quantum nonlocality
The quantum framework is in some respects deeper than spacetime - the information flows which are deployed by the framework are difficult to characterize in spacetime terms.

"Before the measurement there is no particle pair; there is only a gigantic atom. This atom pervades all space. The experiment dematerializes the atom, and in its place two particles appear. Each materializes, as it must in the universe, so as to preserve the laws of nature."

Marvin Chester, Primer of Quantum Mechanics

Generally, physical systems have global properties which continue to evolve globally even as the system becomes spatially separated - when the "parts" of the system are measured then they will manifest correlations which embody (or "cash in") the previous global state. Might these correlations be the result of local processes, perhaps involving other, unknown or "hidden" facts about nature? No. (This is precisely what John Bell proved, in 1964.)

The process generating the correlations is "nonlocal".

Can it be used for signalling then? No. Given quantum theory signalling via the quantum process is not in the cards...

The history of nonlocality

Einstein, Podolsky and Rosen first focused attention on correlated, spatially extended quantum systems in 1935, though in their argument they assumed 'locality' in order to find fault with quantum theory. 25 years later Bell's result showed that EPR's assumption was mistaken. In 1989, Greenberger, Horne and Zeilinger sharpened Bell's results further by considering correlated states with 3 or more entangled particles.

EPR Bell's theorem

Kochen and Specker
GHZ Mermin

There is a relation between the kind of entangled states considered in these proofs and the phenomenon of quantum computation.

How deep does it go?

The full extent of nonlocality as a physical fact is not well understood - for example, does a superfluid exhibit nonlocality? Generally, almost any "collapse of a wavefunction" appears to be nonlocal: is this an artifact of our description?

Since the 1964 analysis of John Bell (Bell's theorem) it is widely recognized that in some sense the nonlocality is real - quantum mechanics is a much different theory than one could assemble with local parts. In the words of Henry Stapp (1977),

"The present formulation asserts that a theory entails a nonlocal connection if there is no conceivable way for the results in each region to be independent of the choice made in the other region. Quantum theory has such a nonlocal connection: That is what Bell actually discovered."

It is probably not possible to signal using quantum nonlocality, though in my view it is a complete mistake to conclude from this that all of the nonlocality "washes out" in practice. (In fact it does not wash out!)

One could turn the question around by viewing the quantum description as completely global, and ask what is the root of the apparent, provisional locality.

What is at the root of nonlocality?
"That the guiding wave, in the general case, propagates not in ordinary three-space but in multidimensional-configuration space is the origin of the notorious 'nonlocality' of quantum mechanics..."
John Bell

Speakable and unspeakable
in quantum mechanics

Other Topics...