Spatial Leggett-Garg inequalities

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 is especially suitable to test the ability of quantum devices to generate spatio-temporal correlations in a Hamiltonian-agnostic manner. 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 is readily observable in current quantum simulation platforms, particularly Rydberg atoms arrays and ultracold atoms in optical lattices. In outlook, spatial Leggett-Garg inequalities constitute a practical tool for benchmarking the complex non-relativistic dynamics of many-body quantum systems.

Quantum Physics (quant-ph); Quantum Gases (cond-mat.quant-gas)

arXiv:2507.03440 [quant-ph]

(or arXiv:2507.03440v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2507.03440 Focus to learn more arXiv-issued DOI via DataCite

Phys. Rev. A 114, 022446 (2026)

https://doi.org/10.1103/k8g5-crbz Focus to learn more DOI(s) linking to related resources

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.