On the Dynamics of Local Hidden-Variable Models

TL;DR

This paper investigates whether local hidden-variable models can describe the time evolution of quantum correlations, proposing that such models generally cannot exist, revealing a new form of nonlocality in quantum dynamics.

Contribution

It introduces the concept of dynamical LHV models, provides a counterexample and a no-go theorem, and suggests a new type of nonlocality based on correlation evolution.

Findings

Dynamical LHV models do not always exist.

A counterexample demonstrates limitations of evolving hidden variables.

A no-go theorem supports the non-existence of such models in general.

Abstract

Bell nonlocality is an intriguing property of quantum mechanics with far reaching consequences for information processing, philosophy and our fundamental understanding of nature. However, nonlocality is a statement about static correlations only. It does not take into account dynamics, i.e. time evolution of those correlations. Consider a dynamic situation where the correlations remain local for all times. Then at each moment in time there exists a local hidden-variable (LHV) model reproducing the momentary correlations. Can the time evolution of the correlations then be captured by evolving the hidden variables? In this light, we define dynamical LHV models and motivate and discuss potential additional physical and mathematical assumptions. Based on a simple counter example we conjecture that such LHV dynamics does not always exist. This is further substantiated by a rigorous no-go theorem. Our results suggest a new type of nonlocality that can be deduced from the observed time evolution of measurement statistics and which generically occurs in interacting quantum systems.