No-go theorem for the composition of quantum systems

TL;DR

This paper presents a no-go theorem that challenges the assumptions underlying the composition of quantum systems in hidden-variables theories, extending the implications of the Pusey-Barrett-Rudolph theorem.

Contribution

It generalizes the Pusey-Barrett-Rudolph theorem to a broad class of deterministic hidden-variables theories, questioning the natural assumptions about subsystem composition.

Findings

Doubts about the 'preparation independence' assumption in hidden-variables models

Constraints on modeling tensor-product states in nonentangled systems

Similar compositional constraints as those found in Bell and Bell-Kochen-Specker theorems

Abstract

Building on the Pusey-Barrett-Rudolph theorem, we derive a no-go theorem for a vast class of deterministic hidden-variables theories, including those consistent on their targeted domain. The strength of this result throws doubt on seemingly natural assumptions (like the "preparation independence" of the Pusey-Barrett-Rudolph theorem) about how "real states" of subsystems compose for joint systems in nonentangled states. This points to constraints in modeling tensor-product states, similar to constraints demonstrated for more complex states by the Bell and Bell-Kochen-Specker theorems.