# Classical-hidden-variable description for entanglement dynamics of two-qubit pure states

## TL;DR

This paper constructs a hidden-variable model for two-qubit pure states that accurately describes short-time entanglement dynamics but cannot reproduce quantum nonlocality, highlighting the distinction between entanglement and nonlocality.

## Contribution

It introduces a Liouvillian-based hidden-variable model for two-qubit pure states and analyzes its limitations in reproducing quantum correlations.

## Key findings

- Model describes short-time entanglement dynamics accurately.
- Model cannot violate Bell inequalities.
- Entanglement and nonlocality are shown to be nonequivalent in this context.

## Abstract

A hidden-variable model is explicitly constructed by use of a Liouvillian description for the dynamics of two coupled spin-1/2 particles. In this model, the underlying Hamiltonian trajectories play the role of deterministic hidden variables, whereas the shape of the initial probability distribution figures as a hidden variable that regulates the capacity of the model in producing correlations. We show that even though the model can very well describe the short-time entanglement dynamics of initially separated pure states, it is incapable of violating the Clauser-Horne-Shimony-Holt inequality. Our work suggests that, if one takes the reluctance of a given quantum resource to be emulated by a local-hidden-variable model as a signature of its nonclassicality degree, then one can conclude that entanglement and nonlocality are nonequivalent even in the context of two-qubit pure states.