Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2207.00605 · Journal of High Energy Physics

Entanglement witnessing for lattice gauge theories

Veronica Panizza, Ricardo Costa de Almeida, Philipp Hauke

Published Sep 22, 2022• 6 citations
arXivHTMLPDF

Abstract

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 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.

DOI
10.1007/jhep09(2022)196

Related papers

Superselection-Resolved Entanglement in Lattice Gauge Theories: A Tensor Network Approach

Noa Feldman, Johannes Knaute, Erez Zohar +1 more

Lattice gauge theories (LGT) play a central role in modern physics, providing insights into high-energy physics, condensed matter physics, and quantum computation. Due to the nontrivial structure of the Hilbert space of LGT systems, entanglement in such systems is tricky to define. However, when one limits themselves to superselection-resolved entanglement, that is, entanglement corresponding to specific gauge symmetry sectors (commonly denoted as superselection sectors), this problem disappears, and the entanglement becomes well-defined. The study of superselection-resolved entanglement is interesting in LGT for an additional reason: when the gauge symmetry is strictly obeyed, superselection-resolved entanglement becomes the only distillable contribution to the entanglement. In our work, we study the behavior of superselection-resolved entanglement in LGT systems. We employ a tensor network construction for gauge-invariant systems as defined by Zohar and Burrello (2016) and find that, in a vast range of cases, the leading term in superselection-resolved entanglement depends on the number of corners in the partition, that is, corner-law entanglement. To our knowledge, this is the first case of such a corner-law being observed in any lattice system.

arXiv:2401.01942•Jan 3, 2024•0 citations

Superselection-resolved entanglement in lattice gauge theories: a tensor network approach

Noa Feldman, Johannes Knaute, Erez Zohar +1 more

A bstract Lattice gauge theories (LGT) play a central role in modern physics, providing insights into high-energy physics, condensed matter physics, and quantum computation. Due to the nontrivial structure of the Hilbert space of LGT systems, entanglement in such systems is tricky to define. However, when one limits themselves to superselection-resolved entanglement, that is, entanglement corresponding to specific gauge symmetry sectors (commonly denoted as superselection sectors), this problem disappears, and the entanglement becomes well-defined. The study of superselection-resolved entanglement is interesting in LGT for an additional reason: when the gauge symmetry is strictly obeyed, superselection-resolved entanglement becomes the only distillable contribution to the entanglement. In our work, we study the behavior of superselection-resolved entanglement in LGT systems. We employ a tensor network construction for gauge-invariant systems as defined by Zohar and Burrello [1] and find that, in a vast range of cases, the leading term in superselection-resolved entanglement depends on the number of corners in the partition — corner-law entanglement. To our knowledge, this is the first case of such a corner-law being observed in any lattice system.

Journal of High Energy Physics•May 8, 2024•6 citations

Magic of discrete lattice gauge theories

Gianluca Esposito, Simone Cepollaro, Luigi Cappiello +1 more

Simulation of quantum field theories and fundamental interactions are one of the most challenging tasks in modern particle physics. Classical computers generally fail to reproduce accurate results when it comes to strongly coupled theories such as QCD. Recent developments in quantum technologies open up the possibility of simulating such physical regimes by using quantum computers. In this paper, we study the quantum resource related to the simulability of a quantum theory, i.e. non-stabilizerness for Lattice Gauge Theory (LGT) with discrete symmetry gauge groups. We show that enforcing gauge constraints for $\mathbb{Z}_l$ LGTs has no cost in terms of this resource and discuss the relation between non-abelianity of the gauge group with the average non-stabilizerness of the gauge invariant Hilbert space.

hep-latCross-listedarXiv:2601.15842•International Journal of Geometric Methods in Modern Physics•Jan 23, 2026•2 citations

Entanglement entropy in lattice gauge theories

P. V. Buividovich, M I Polikarpov

We report on the recent progress in theoretical and numerical studies of entanglement entropy in lattice gauge theories. It is shown that the concept of quantum entanglement between gauge fields in two complementary regions of space can only be introduced if the Hilbert space of physical states is extended in a certain way. In the extended Hilbert space, the entanglement entropy can be partially interpreted as the classical Shannon entropy of the flux of the gauge fields through the boundary between the two regions. Such an extension leads to a reduction procedure which can easily be implemented in lattice simulations by constructing lattices with special topology. This enables us to measure the entanglement entropy in lattice Monte-Carlo simulations. On the simplest example of Z 2 lattice gauge theory in dimensions we demonstrate the relation between the entanglement entropy and the classical entropy of the field flux. For lattice gauge theory in four dimensions, we find a signature of non-analytic dependence of the entanglement entropy on the size of the region. We also comment on the holographic interpretation of the entanglement entropy.

arXiv:0811.3824•Journal of Physics A Mathematical and Theoretical•Jul 14, 2009•26 citations

Entanglement entropy in lattice gauge theories

P. V. Buividovich

We report on the recent progress in theoretical and numerical studies of entanglement entropy in lattice gauge theories.It is shown that the concept of quantum entanglement between gauge fields in two complementary regions of space can only be introduced if the Hilbert space of physical states is extended in a certain way.In the extended Hilbert space, the entanglement entropy can be partially interpreted as the classical Shannon entropy of the flux of the gauge fields through the boundary between the two regions.Such an extension leads to a reduction procedure which can be easily implemented in lattice simulations by constructing lattices with special topology.This enables us to measure the entanglement entropy in lattice Monte-Carlo simulations.On the simplest example of Z 2 lattice gauge theory in (2 + 1) dimensions we demonstrate the relation between entanglement entropy and the classical entropy of the field flux.For SU (2) lattice gauge theory in four dimensions, we find a signature of non-analytic dependence of the entanglement entropy on the size of the region.We also comment on the holographic interpretation of the entanglement entropy.

Conference on Quark Confinement and the Hadron Spectrum (Confinement)•Sep 12, 2012•6 citations

Lattice gauge theory simulations in the quantum information era

M. Dalmonte, Simone Montangero

The many-body problem is ubiquitous in the theoretical description of physical phenomena, ranging from the behaviour of elementary particles to the physics of electrons in solids. Most of our understanding of many-body systems comes from analysing the symmetric properties of Hamiltonian and states: the most striking examples are gauge theories such as quantum electrodynamics, where a local symmetry strongly constrains the microscopic dynamics. The physics of such gauge theories is relevant for the understanding of a diverse set of systems, including frustrated quantum magnets and the collective dynamics of elementary particles within the standard model. In the last few years, several approaches have been put forward to tackle the complex dynamics of gauge theories using quantum information concepts. In particular, quantum simulation platforms have been put forward for the realisation of synthetic gauge theories, and novel classical simulation algorithms based on quantum information concepts have been formulated. In this review, we present an introduction to these approaches, illustrating the basics concepts and highlighting the connections between apparently very different fields, and report the recent developments in this new thriving field of research.

arXiv:1602.03776•Contemporary Physics•Mar 9, 2016•272 citations
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 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.
Lattice gauge theories (LGT) play a central role in modern physics, providing insights into high-energy physics, condensed matter physics, and quantum computation. Due to the nontrivial structure of the Hilbert space of LGT systems, entanglement in such systems is tricky to define. However, when one limits themselves to superselection-resolved entanglement, that is, entanglement corresponding to specific gauge symmetry sectors (commonly denoted as superselection sectors), this problem disappears, and the entanglement becomes well-defined. The study of superselection-resolved entanglement is interesting in LGT for an additional reason: when the gauge symmetry is strictly obeyed, superselection-resolved entanglement becomes the only distillable contribution to the entanglement. In our work, we study the behavior of superselection-resolved entanglement in LGT systems. We employ a tensor network construction for gauge-invariant systems as defined by Zohar and Burrello (2016) and find that, in a vast range of cases, the leading term in superselection-resolved entanglement depends on the number of corners in the partition, that is, corner-law entanglement. To our knowledge, this is the first case of such a corner-law being observed in any lattice system.
A bstract Lattice gauge theories (LGT) play a central role in modern physics, providing insights into high-energy physics, condensed matter physics, and quantum computation. Due to the nontrivial structure of the Hilbert space of LGT systems, entanglement in such systems is tricky to define. However, when one limits themselves to superselection-resolved entanglement, that is, entanglement corresponding to specific gauge symmetry sectors (commonly denoted as superselection sectors), this problem disappears, and the entanglement becomes well-defined. The study of superselection-resolved entanglement is interesting in LGT for an additional reason: when the gauge symmetry is strictly obeyed, superselection-resolved entanglement becomes the only distillable contribution to the entanglement. In our work, we study the behavior of superselection-resolved entanglement in LGT systems. We employ a tensor network construction for gauge-invariant systems as defined by Zohar and Burrello [1] and find that, in a vast range of cases, the leading term in superselection-resolved entanglement depends on the number of corners in the partition — corner-law entanglement. To our knowledge, this is the first case of such a corner-law being observed in any lattice system.
Simulation of quantum field theories and fundamental interactions are one of the most challenging tasks in modern particle physics. Classical computers generally fail to reproduce accurate results when it comes to strongly coupled theories such as QCD. Recent developments in quantum technologies open up the possibility of simulating such physical regimes by using quantum computers. In this paper, we study the quantum resource related to the simulability of a quantum theory, i.e. non-stabilizerness for Lattice Gauge Theory (LGT) with discrete symmetry gauge groups. We show that enforcing gauge constraints for Zl\mathbb{Z}_lZl​ LGTs has no cost in terms of this resource and discuss the relation between non-abelianity of the gauge group with the average non-stabilizerness of the gauge invariant Hilbert space.
We report on the recent progress in theoretical and numerical studies of entanglement entropy in lattice gauge theories. It is shown that the concept of quantum entanglement between gauge fields in two complementary regions of space can only be introduced if the Hilbert space of physical states is extended in a certain way. In the extended Hilbert space, the entanglement entropy can be partially interpreted as the classical Shannon entropy of the flux of the gauge fields through the boundary between the two regions. Such an extension leads to a reduction procedure which can easily be implemented in lattice simulations by constructing lattices with special topology. This enables us to measure the entanglement entropy in lattice Monte-Carlo simulations. On the simplest example of Z 2 lattice gauge theory in dimensions we demonstrate the relation between the entanglement entropy and the classical entropy of the field flux. For lattice gauge theory in four dimensions, we find a signature of non-analytic dependence of the entanglement entropy on the size of the region. We also comment on the holographic interpretation of the entanglement entropy.
We report on the recent progress in theoretical and numerical studies of entanglement entropy in lattice gauge theories.It is shown that the concept of quantum entanglement between gauge fields in two complementary regions of space can only be introduced if the Hilbert space of physical states is extended in a certain way.In the extended Hilbert space, the entanglement entropy can be partially interpreted as the classical Shannon entropy of the flux of the gauge fields through the boundary between the two regions.Such an extension leads to a reduction procedure which can be easily implemented in lattice simulations by constructing lattices with special topology.This enables us to measure the entanglement entropy in lattice Monte-Carlo simulations.On the simplest example of Z 2 lattice gauge theory in (2 + 1) dimensions we demonstrate the relation between entanglement entropy and the classical entropy of the field flux.For SU (2) lattice gauge theory in four dimensions, we find a signature of non-analytic dependence of the entanglement entropy on the size of the region.We also comment on the holographic interpretation of the entanglement entropy.
The many-body problem is ubiquitous in the theoretical description of physical phenomena, ranging from the behaviour of elementary particles to the physics of electrons in solids. Most of our understanding of many-body systems comes from analysing the symmetric properties of Hamiltonian and states: the most striking examples are gauge theories such as quantum electrodynamics, where a local symmetry strongly constrains the microscopic dynamics. The physics of such gauge theories is relevant for the understanding of a diverse set of systems, including frustrated quantum magnets and the collective dynamics of elementary particles within the standard model. In the last few years, several approaches have been put forward to tackle the complex dynamics of gauge theories using quantum information concepts. In particular, quantum simulation platforms have been put forward for the realisation of synthetic gauge theories, and novel classical simulation algorithms based on quantum information concepts have been formulated. In this review, we present an introduction to these approaches, illustrating the basics concepts and highlighting the connections between apparently very different fields, and report the recent developments in this new thriving field of research.