Two or more separate parties conducting measurements over a quantum state can observe correlations which cannot be explained with any local hidden variable theory.
[5] This research program has so far provided a generalization of Bell's theorem that allows falsifying all classical theories with a superluminal, yet finite, hidden influence.
There is an on-going debate on whether the wave-function represents the epistemic state of a yet to be discovered ontic variable or, on the contrary, it is a fundamental entity.
[9] Note that, in QBism[10] and Copenhagen-type[11] views, quantum states are still regarded as epistemic, not with respect to some ontic variable, but to one's expectations about future experimental outcomes.
Some of the counter-intuitive aspects of quantum theory, as well as the difficulty to extend it, follow from the fact that its defining axioms lack a physical motivation.
[12] Notably, a small set of physically motivated axioms is enough to single out the GPT representation of quantum theory.
[13] L. Hardy introduced the concept of GPT in 2001, in an attempt to re-derive quantum theory from basic physical principles.
[14] The work of Dakic and Brukner eliminated this “axiom of simplicity” and provided a reconstruction of quantum theory based on three physical principles.
The drawback of the device-independent approach is that, even when taken together, all the afore-mentioned physical principles do not suffice to single out the set of quantum correlations.
[29] Such theories provide an explanation to the nonexistence of superpositions of macroscopic objects, at the cost of abandoning unitarity and exact energy conservation.
In Sorkin's quantum measure theory (QMT), physical systems are not modeled via unitary rays and Hermitian operators, but through a single matrix-like object, the decoherence functional.
In view of this trend, it is reasonable to postulate that any high-order map from quantum instruments (namely, measurement processes) to probabilities should also be physically realizable.
The starting point of this claim is the following mental experiment: two parties, Alice and Bob, enter a building and end up in separate rooms.