On the Dynamics of Local Hidden-Variable Models

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 a wide range of physical and mathematical assumptions. Based on a simple counter example we conjecture that such LHV dynamics does in general not exist. This is further substantiated by a rigorous no-go theorem. Our results suggest a new type of dynamical nonlocality expressed by the quantum time evolution of local correlations.