Is a description deeper than the quantum one possible?

TL;DR

This paper challenges the assumption that quantum mechanics is complete by analyzing the free choice condition and explores how crypto-nonlocal hidden variables can extend beyond standard quantum predictions for two-qubit systems.

Contribution

It demonstrates that the completeness of quantum mechanics depends on a stronger-than-necessary free choice assumption and characterizes potential deviations using crypto-nonlocal hidden variables.

Findings

Quantum completeness depends on a strong free choice assumption.

Crypto-nonlocal hidden variables can describe maximal deviations from quantum mechanics.

The interpretation of the quantum state remains unresolved.

Abstract

Recently, it has been argued that quantum mechanics is a complete theory, and that different quantum states do necessarily correspond to different elements of reality, under the assumptions that quantum mechanics is correct and that measurement settings can be freely chosen. In this work, we prove that this result is a consequence of an unnecessarily strong mathematical expression of the free choice assumption, which embodies more conditions than explicitly stated. The issues of the completeness of quantum mechanics, and of the interpretation of the state vector, are by no means resolved. Taking this perspective, we describe how the recently introduced class of crypto-nonlocal hidden variables theories can be used to characterize the maximal possible departure from quantum mechanics, when the system consists of a pair of qubits.