On the completeness of quantum mechanics and the interpretation of the state vector

TL;DR

This paper challenges the assumption that quantum states uniquely correspond to reality, showing that under weaker free choice assumptions, multiple states can relate to the same reality, questioning the completeness of quantum mechanics.

Contribution

It identifies hidden assumptions in previous arguments for quantum completeness and presents a model where different quantum states share the same underlying reality.

Findings

Hidden assumptions limit previous results

A model reproduces quantum mechanics with shared realities

Different quantum states can correspond to the same reality

Abstract

Recently, it has been argued that quantum mechanics is complete, and that quantum states vectors are necessarily in one-to-one correspondence with the elements of reality, under the assumptions that quantum theory is correct and that measurement settings can be freely chosen. In this work, we argue that the adopted form of the free choice assumption is stronger than needed. We unveil hidden assumptions underlying these results, which limit their range of validity. We support our argument by a model for the bipartite two-level system, reproducing quantum mechanics, in which the free will assumption is respected, and different quantum states can be connected to the same state of reality.