No extension of quantum theory can have improved predictive power

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.

6 pages plus 7 of supplementary material, 3 figures. Title changed. Added discussion on Bell's notion of locality. FAQ answered at http://perimeterinstitute.ca/personal/rcolbeck/FAQ.html

References in corpus (10)

• The Free Will Theorem
• The Communication Cost of Simulating Bell Correlations
• Testing quantum correlations versus single-particle properties within Leggett's model and beyond
• Hidden variable models for quantum theory cannot have any local part
• Relative States and the Environment: Einselection, Envariance, Quantum Darwinism, and the Existential Interpretation
• Simulation of partial entanglement with nonsignaling resources
• Bell's Theory with no Locality assumption
• Derivation of Bell's locality condition from the relativity of simultaneity
• Comment on 'Non-realism: deep thought or soft option?', by N. Gisin
• Why aren't quantum correlations maximally nonlocal? Biased local randomness as essential feature of quantum mechanics

Cited by in corpus (4)

• Unconditionally secure device-independent quantum key distribution with only two devices
• Onthological models predictively inequivalent to quantum theory
• A short note on the concept of free choice
• Comment on "Quantum theory cannot be extended" [arXiv:1005.5173v1]: Falsification of non-covariant extensions requires the before-before experiment