Entanglement Witnessing for Lattice Gauge Theories

TL;DR

This paper develops a theoretical framework for witnessing entanglement in lattice gauge theories, addressing the challenge posed by gauge constraints, and demonstrates its application to a 2+1D U(1) gauge theory, enabling resource-efficient entanglement certification.

Contribution

It introduces a novel entanglement witnessing method tailored for lattice gauge theories, accounting for superselection rules, facilitating efficient entanglement certification in simulations.

Findings

Framework applicable to U(1) lattice gauge theories in 2+1D

Circumvents costly state tomography methods

Enables resource-efficient entanglement certification

Abstract

Entanglement is assuming a central role in modern quantum many-body physics. Yet, for lattice gauge theories its certification remains extremely challenging. A key difficulty stems from the local gauge constraints underlying the gauge theory, which separate the full Hilbert space into a direct sum of subspaces characterized by different superselection rules. In this work, we develop the theoretical framework of entanglement witnessing for lattice gauge theories that takes this subtlety into account. We illustrate the concept at the example of a $\mathrm{U}(1)$ lattice gauge theory in 2+1 dimensions, without and with dynamical fermionic matter. As this framework circumvents costly state tomography, it opens the door to resource-efficient certification of entanglement in theoretical studies as well as in laboratory quantum simulations of gauge theories.