The completeness of quantum theory for predicting measurement outcomes

TL;DR

This paper reviews recent work showing that quantum theory is maximally informative and complete, as no alternative compatible theories can provide better predictions, establishing the one-to-one correspondence with quantum states.

Contribution

It demonstrates that quantum theory is complete by proving no alternative theories can outperform it under certain constraints.

Findings

Quantum theory is maximally informative.

Any alternative maximally informative theory is equivalent to quantum theory.

Quantum states are in one-to-one correspondence with system states.

Abstract

The predictions that quantum theory makes about the outcomes of measurements are generally probabilistic. This has raised the question whether quantum theory can be considered complete, or whether there could exist alternative theories that provide improved predictions. Here we review recent work that considers arbitrary alternative theories, constrained only by the requirement that they are compatible with a notion of "free choice" (defined with respect to a natural causal order). It is shown that quantum theory is "maximally informative", i.e., there is no other compatible theory that gives improved predictions. Furthermore, any alternative maximally informative theory is necessarily equivalent to quantum theory. This means that the state a system has in such a theory is in one-to-one correspondence with its quantum-mechanical state (the wave function). In this sense, quantum theory is complete.