Why $\psi$ is incomplete indeed: a simple illustration

TL;DR

This paper discusses the incompleteness of the quantum state vector $\\psi$ and suggests that completing it requires specifying measurement context rather than hidden variables, offering an alternative view on Bell's inequalities.

Contribution

It proposes that the incompleteness of the quantum state vector $\\psi$ can be addressed by including measurement context, challenging the common interpretation of quantum non-locality.

Findings

Revisits the EPR argument on quantum state incompleteness

Highlights the importance of measurement context in quantum description

Provides a simple illustration with two qubits

Abstract

With the Nobel Prize attributed to Aspect, Clauser, and Zeilinger, the international scientific community acknowledged the fundamental importance of the experimental violation of Bell's inequalities. It is however still debated what fails in Bell's hypotheses, leading to these inequalities, and usually summarized as "local realism", or maybe more appropriately "classical local realism". The most common explanation is "quantum non-locality", that remains however fully compatible with relativistic causality; this makes wondering whether any non-local phenomenon is really involved in these experiments. Here we want to recapitulate another option, sometimes called "predictive incompleteness", closely related to the idea that the usual state vector $\psi$ is incomplete indeed, as it was claimed by Einstein, Podolsky and Rosen. However, the right way to complete $\psi$ has nothing to do with hidden variables, but requires to specify the measurement context, as it was claimed by Bohr. Here we will consider the simple case of two spin 1/2, or two qubits, in order to keep the argument simple, but it does apply generally in quantum mechanics.