Leggett's theorem without inequalities

TL;DR

This paper proves a no-go theorem ruling out certain hidden variables theories that satisfy parameter independence for maximally entangled states in high-dimensional quantum systems, extending Leggett's inequality results.

Contribution

It introduces a new no-go theorem that excludes a class of hidden variables models satisfying parameter independence, without relying on inequalities.

Findings

No non-trivial hidden variables models for maximally entangled states in dimensions ≥ 3x3

The theorem extends Leggett's inequality-based results to a broader class of theories

Supports the non-classical nature of quantum correlations

Abstract

We prove a no-go theorem for a class of hidden variables theories that satisfy parameter independence. Specifically, we show that, assuming two conditions, there are no non-trivial hidden variables models of the quantum predictions for product measurements on two systems in any maximally entangled state in a Hilbert space of dimension at least 3x3. The two conditions are parameter independence and a condition that we call conditional parameter independence. The result is analogous to the recent no-go theorems based on Leggett's inequalities and their generalisations.