2025/07/04 by Müller-Rigat, Guillem, Farina, Donato, Lewenstein, Maciej +1
#FOS: Physical sciences #Quantum Gases (cond-mat.quant-gas) #Quantum Physics (quant-ph)
paper · doi:10.48550/arxiv.2507.03440
We formulate a spatial extension of the Leggett-Garg inequality by considering three distant observers locally measuring a many-body system at three subsequent times. The spatial form, in particular, is specially suited to analyze propagation of quantum perturbations through spin chains, by capturing how a measurement at one site can later affect distant sites due to the interactions. We illustrate our proposal for a Heisenberg chain in a magnetic field, showing indeed that the first inequality-violation time scales proportionally to the distance between measuring parties. We attribute this phenomenon to Lieb-Robinson physics and, confirming this connection, we find that violations are anticipated when increasing the interaction range. The inequality violation, readily observable in current experiments, demonstrates the incompatibility between two-point correlation functions and the macrorealistic hypothesis. In outlook, spatial Leggett-Garg inequalities constitute a new tool for analyzing the non-relativistic dynamics of many-body quantum systems.