Quantum physics cannot be captured by classical linear hidden variable theories even in the absence of entanglement

TL;DR

This paper demonstrates that quantum systems exhibit complex time correlations that cannot be replicated by classical linear hidden variable theories, even without entanglement, highlighting fundamental differences in quantum and classical models.

Contribution

The study introduces Hidden Quantum Markov Models and shows they produce more complex correlations than classical Hidden Markov Models, proving quantum physics cannot be simulated by linear hidden variables.

Findings

Quantum trajectories of a single qubit show complex correlations.

Hidden Quantum Markov Models outperform classical models in correlation complexity.

Quantum physics cannot be replaced by linear hidden variable theories.

Abstract

Recent experimental tests of Bell inequalities confirm that entangled quantum systems cannot be described by local classical theories but still do not answer the question whether or not quantum systems could in principle be modelled by linear hidden variable theories. In this paper, we study the quantum trajectories of a single qubit that experiences a sequence of repeated generalised measurements. It is shown that this system, which constitutes a Hidden Quantum Markov Model, is more likely to produce complex time correlations than any classical Hidden Markov Model with two output symbols. From this, we conclude that quantum physics cannot be replaced by linear hidden variable theories. Indeed, it has already been recognised that not only entanglement but also non-classical time correlations of quantum systems with quantum feedback are a valuable resource for quantum technology applications.