No extension of quantum theory can have improved predictive power

TL;DR

This paper proves that no extension of quantum theory can provide better predictive power than quantum mechanics itself, reaffirming its maximal informational content under free measurement choices.

Contribution

It establishes that quantum theory cannot be improved upon for predictive accuracy, even with potential extensions, assuming free measurement choices.

Findings

No extension of quantum theory can outperform quantum mechanics in prediction.

Quantum theory's predictive power is maximally informative under free measurement assumptions.

Results impact quantum foundations and cryptography by confirming inherent randomness is fundamental.

Abstract

According to quantum theory, measurements generate random outcomes, in stark contrast with classical mechanics. This raises the question of whether there could exist an extension of the theory which removes this indeterminism, as suspected by Einstein, Podolsky and Rosen (EPR). Although this has been shown to be impossible, existing results do not imply that the current theory is maximally informative. Here we ask the more general question of whether any improved predictions can be achieved by any extension of quantum theory. Under the assumption that measurements can be chosen freely, we answer this question in the negative: no extension of quantum theory can give more information about the outcomes of future measurements than quantum theory itself. Our result has significance for the foundations of quantum mechanics, as well as applications to tasks that exploit the inherent randomness in quantum theory, such as quantum cryptography.