Spatial Leggett-Garg Inequalities

• URL: http://arxiv.org/abs/2507.03440v1
• Date: Fri, 04 Jul 2025 09:55:49 GMT
• Title: Spatial Leggett-Garg Inequalities
• Authors: Guillem Müller-Rigat, Donato Farina, Maciej Lewenstein, Andrea Tononi,
• Abstract summary: We extend the Leggett-Garg inequality by considering three distant observers locally measuring a many-body system at three subsequent times.<n>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.<n>In outlook, spatial Leggett-Garg inequalities constitute a new tool for analyzing the non-relativistic dynamics of many-body quantum systems.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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