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:2603.28877 · APS Open Science

Effects of measurements on entanglement dynamics for $1+1$D $\mathbb Z_2$ lattice gauge theory

Nilachal Chakrabarti, Nisa Ara, Neha Nirbhan, Arpan Bhattacharyya, Indrakshi Raychowdhury

quant-phcond-mat.str-elhep-lathep-thSubmitted Mar 30, 2026• Announced Apr 1, 2026• 0 citations
v1 · Mar 30, 2026v2 · Aug 3, 2026
arXivHTMLPDF

Abstract

The $1+1$ dimensional $\mathbb Z_2$ gauge theory is the simplest model that allows for quantum simulation to probe the fundamental aspects of a gauge theory coupled with dynamical fermions. To reliably benchmark such a system, it is crucial to understand the non-unitary quantum dynamics arising from the underlying non-Hermitian evolution and to model the effects of quantum measurements. This work focuses on measuring physical observables for a $\mathbb Z_2$ gauge theory. Tensor network calculations are performed to probe the effect of measurement for larger lattice sizes (up to 256-site systems). Using Matrix Product State calculations, the dynamics of entanglement entropy are studied as a function of the measurement rate and the coupling constant. We find that, under both local and non-local measurements, the late-time saturation value of the bipartite entanglement entropy remains independent of system size, indicating the absence of a measurement-induced phase transition in the no-click limit.

Journal reference
APS Open Science, 1, 000118 (2026)
DOI
10.1103/1tmj-fftr
Comments
26 pages, 15 figures

Related papers

Dynamics of entanglement entropy for a locally monitored lattice gauge theory

Nisa Ara, Arpan Bhattacharyya, Nilachal Chakrabarti +2 more

The $1+1$ dimensional $Z_2$ gauge theory is the simplest model that allows for quantum computation or quantum simulation to probe the fundamental aspects of a gauge theory coupled with dynamical fermions. To reliably benchmark such a system, it is crucial to understand the non-unitary quantum dynamics arising from the underlying non-Hermitian evolution and to model the effects of quantum measurements. In this work, we study post-selected filtering dynamics of physical observables for a $\mathbb {Z} _2$ gauge theory. Tensor network calculations are performed to dynamically probe entanglement entropy at larger lattice sizes. We report that projective measurement of local and diagonal observables (electric and mass energy densities) in the computational basis demonstrates the absence of any measurement-induced phase transition like phenomenon, as indicated by the system-size independence of the late-time saturation value of the bipartite entanglement entropy.

quant-pharXiv:2603.29900•Apr 1, 2026•0 citations

Dynamics of entanglement entropy for a locally monitored lattice gauge theory

Nisa Ara, Arpan Bhattacharyya, Nilachal Chakrabarti +2 more

The $1+1$ dimensional $Z_2$ gauge theory is the simplest model that allows for quantum computation or quantum simulation to probe the fundamental aspects of a gauge theory coupled with dynamical fermions. To reliably benchmark such a system, it is crucial to understand the non-unitary quantum dynamics arising from the underlying non-Hermitian evolution and to model the effects of quantum measurements. This work focuses on monitoring ultra-local physical observables for a $\mathbb Z_2$ gauge theory. Tensor network calculations are performed to dynamically probe entanglement entropy at larger lattice sizes. In this work, we report that continuously monitoring local and diagonal observables (electric and mass energy densities) in the computational basis demonstrates the absence of any measurement-induced phase transition, as indicated by the system-size independence of the late-time saturation value of the bipartite entanglement entropy.

International Symposium on Lattice Field Theory (LATTICE)•Jul 5, 2026•1 citation

Magic and entanglement in 1+1-dimensional SU(2) lattice gauge theory

Raghav G. Jha, Goksu C. Toga, Jaber I. Taher +2 more

Entanglement and non-stabilizerness (magic) quantify two distinct departures of quantum systems from classical description: the former measures non-local correlations, while the latter measures the deviation from stabilizer states that can be efficiently simulated classically. Understanding magic in physically relevant quantum field theories is essential for identifying where quantum advantage may be realized in the early fault-tolerant quantum computing era. We calculate the gauge-invariant entanglement entropy and stabilizer Rényi entropy of the ground state of the (1+1)-dimensional SU(2) lattice gauge theory formulated in a dressed-site basis that enforces Gauss's law exactly. Using tensor networks, we obtain results for system sizes up to $L=100$ (300 qubits). We find a crossover denoted by $g_{\star}$ where the ground state passes from a more magic-rich regime into a regime with less magic; this is also tracked by the sharpest change of both the entanglement entropy and lattice particle density. Our large-scale study of non-stabilizerness and entanglement entropy in a non-Abelian lattice gauge theory with matter provides new insight into the interplay of magic and entanglement in gauge theories, both of which are relevant for classical and early fault-tolerant quantum simulations.

quant-pharXiv:2606.09971•Jun 10, 2026•0 citations

Non-stabilizerness and entanglement in $(2+1)$-dimensional SU(2) lattice gauge theory using tensor networks

Raghav G. Jha, Jaber I. Taher, Muhammad Asaduzzaman +3 more

We study non-stabilizerness (magic) in the ground state of $(2+1)$-dimensional $\mathrm{SU}(2)$ Hamiltonian lattice gauge theory with matter, formulated in the dressed-site basis in the hardcore-gluon truncation and restricted to the zero baryon-number sector. Using matrix product states, we compute three facets of magic: the second-order stabilizer Rényi entropy (SRE) $M_2$, its non-local component $M_2^{\rm NL}$, estimated by the SRE $M_2(\tildeψ)$ of the computational-basis Schmidt representative $\tildeψ$, and a lower bound in terms of the anti-flatness $F$ of the entanglement spectrum. We also prove a stronger form of the sandwich relation: $-\log_2(1-4F)\le M_2^{\rm NL}\le M_2$; the lower bound rests on a stronger inequality that we obtain for arbitrary Schmidt bases and rank, with an optimal constant. Combined with recent results, this yields the unconditional bracket $\max\{-\log_2(1-4F),\,M_2(\tildeψ)-4\}\le M_2^{\rm NL}\le M_2(\tildeψ)$. We emphasize a structural distinction that makes the non-local quantities the physically preferred diagnostics: whereas the full SRE depends on the (non-unique) encoding of the gauge-invariant local Hilbert space into qubits, the non-local magic, its estimate $M_2(\tildeψ)$, and the anti-flatness are invariant under site-local re-encodings and are therefore intrinsic to the state and bipartition. By varying the gauge coupling for two values of the fermion mass on lattices up to $8\times 8$ ($\sim 288$ qubits) with bond dimension up to $128$, we find that the non-local magic, as estimated by $M_2(\tildeψ)$, furnishes a sharper and more bond-dimension-friendly probe of the gauge-matter delocalization crossover compared to the full SRE or the gauge-invariant entanglement entropy, retaining a clear signal at bond dimensions well below those needed to converge the ground state itself.

quant-pharXiv:2609.28634•Sep 25, 2026•0 citations

Measurement-induced entanglement transitions in the quantum Ising chain: From infinite to zero clicks

Xhek Turkeshi, Alberto Biella, Rosario Fazio +2 more

Recent years have witnessed major progress in the understanding of monitored quantum dynamics, an open quantum setting where the environment is a measurement apparatus that probes the system locally. For the resulting quantum trajectory, unitary evolution and local measurements have competing tendencies in the building of quantum correlations: while the coherent interactions in the former increase the entanglement, the resolving nature of the local measurement collapses the state of the system. Here, the authors study the interplay of monitoring and system dynamics by focusing on the monitored quantum Ising chain as the measurement strength is varied, going from the regime of weak detection, corresponding to the limit of infinite small jumps, to the case of post-selected no-jump case. A sharp transition is found between a logarithmic law phase to an area law phase for the entanglement entropy, which occurs at the same value of the measurement rate in the two limiting situations.

arXiv:2103.09138•Physical review. B./Physical review. B•Jun 30, 2021•263 citations

Theory of post-selected entanglement transitions in monitored bosons

Ilia Komissarov, Emanuele G. Dalla Torre, Ahana Chakraborty

Entanglement phase transitions driven by quantum measurements have emerged as a central paradigm in open quantum many-body physics. Such phase transitions are well established for systems with finite local Hilbert-space dimensions, such as qubits and fermions, while their realization in bosonic systems with unbounded local occupation numbers remains poorly understood. Even in the absence of interactions, number states of bosons are intrinsically non-Gaussian, preventing the use of standard correlation-matrix approaches. To address this problem, we develop a replica-free Keldysh field-theoretic framework that expresses the Renyi entropy of bosonic systems initialized in on-site Fock states in terms of permanents of matrices constructed from single-particle Green's functions. Applying this framework to a continuously monitored one-dimensional cross-stitch lattice conditioned on the no-click trajectory, we uncover a transition from volume-law to logarithmic entanglement scaling. We show that the transition is controlled by a restructuring of the non-Hermitian spectrum that changes the number of long-lived modes from extensive to finite. In the strongly monitored regime, bosons dynamically condense into a microscopic number of slowest-decaying modes, producing logarithmic entanglement scaling, whereas an extensive manifold of long-lived modes at weak monitoring gives rise to volume-law entanglement. Our results establish a distinct mechanism for measurement-induced entanglement transitions in free bosonic systems and provide a computationally efficient diagnostic of the measurement-induced bosonic condensation.

quant-pharXiv:2609.19251•Sep 18, 2026•0 citations
Effects of measurements on entanglement dynamics for 1+11+11+1D Z2\mathbb Z_2Z2​ lattice gauge theory
The 1+11+11+1 dimensional Z2\mathbb Z_2Z2​ gauge theory is the simplest model that allows for quantum simulation to probe the fundamental aspects of a gauge theory coupled with dynamical fermions. To reliably benchmark such a system, it is crucial to understand the non-unitary quantum dynamics arising from the underlying non-Hermitian evolution and to model the effects of quantum measurements. This work focuses on measuring physical observables for a Z2\mathbb Z_2Z2​ gauge theory. Tensor network calculations are performed to probe the effect of measurement for larger lattice sizes (up to 256-site systems). Using Matrix Product State calculations, the dynamics of entanglement entropy are studied as a function of the measurement rate and the coupling constant. We find that, under both local and non-local measurements, the late-time saturation value of the bipartite entanglement entropy remains independent of system size, indicating the absence of a measurement-induced phase transition in the no-click limit.
The 1+11+11+1 dimensional Z2Z_2Z2​ gauge theory is the simplest model that allows for quantum computation or quantum simulation to probe the fundamental aspects of a gauge theory coupled with dynamical fermions. To reliably benchmark such a system, it is crucial to understand the non-unitary quantum dynamics arising from the underlying non-Hermitian evolution and to model the effects of quantum measurements. In this work, we study post-selected filtering dynamics of physical observables for a Z2\mathbb {Z} _2Z2​ gauge theory. Tensor network calculations are performed to dynamically probe entanglement entropy at larger lattice sizes. We report that projective measurement of local and diagonal observables (electric and mass energy densities) in the computational basis demonstrates the absence of any measurement-induced phase transition like phenomenon, as indicated by the system-size independence of the late-time saturation value of the bipartite entanglement entropy.
The 1+11+11+1 dimensional Z2Z_2Z2​ gauge theory is the simplest model that allows for quantum computation or quantum simulation to probe the fundamental aspects of a gauge theory coupled with dynamical fermions. To reliably benchmark such a system, it is crucial to understand the non-unitary quantum dynamics arising from the underlying non-Hermitian evolution and to model the effects of quantum measurements. This work focuses on monitoring ultra-local physical observables for a Z2\mathbb Z_2Z2​ gauge theory. Tensor network calculations are performed to dynamically probe entanglement entropy at larger lattice sizes. In this work, we report that continuously monitoring local and diagonal observables (electric and mass energy densities) in the computational basis demonstrates the absence of any measurement-induced phase transition, as indicated by the system-size independence of the late-time saturation value of the bipartite entanglement entropy.
Entanglement and non-stabilizerness (magic) quantify two distinct departures of quantum systems from classical description: the former measures non-local correlations, while the latter measures the deviation from stabilizer states that can be efficiently simulated classically. Understanding magic in physically relevant quantum field theories is essential for identifying where quantum advantage may be realized in the early fault-tolerant quantum computing era. We calculate the gauge-invariant entanglement entropy and stabilizer Rényi entropy of the ground state of the (1+1)-dimensional SU(2) lattice gauge theory formulated in a dressed-site basis that enforces Gauss's law exactly. Using tensor networks, we obtain results for system sizes up to L=100L=100L=100 (300 qubits). We find a crossover denoted by g⋆g_{\star}g⋆​ where the ground state passes from a more magic-rich regime into a regime with less magic; this is also tracked by the sharpest change of both the entanglement entropy and lattice particle density. Our large-scale study of non-stabilizerness and entanglement entropy in a non-Abelian lattice gauge theory with matter provides new insight into the interplay of magic and entanglement in gauge theories, both of which are relevant for classical and early fault-tolerant quantum simulations.
Non-stabilizerness and entanglement in (2+1)(2+1)(2+1)-dimensional SU(2) lattice gauge theory using tensor networks
We study non-stabilizerness (magic) in the ground state of (2+1)(2+1)(2+1)-dimensional SU(2)\mathrm{SU}(2)SU(2) Hamiltonian lattice gauge theory with matter, formulated in the dressed-site basis in the hardcore-gluon truncation and restricted to the zero baryon-number sector. Using matrix product states, we compute three facets of magic: the second-order stabilizer Rényi entropy (SRE) M2M_2M2​, its non-local component M2NLM_2^{\rm NL}M2NL​, estimated by the SRE M2(ψ~)M_2(\tildeψ)M2​(ψ~​) of the computational-basis Schmidt representative ψ~\tildeψψ~​, and a lower bound in terms of the anti-flatness FFF of the entanglement spectrum. We also prove a stronger form of the sandwich relation: −log⁡2(1−4F)≤M2NL≤M2-\log_2(1-4F)\le M_2^{\rm NL}\le M_2−log2​(1−4F)≤M2NL​≤M2​; the lower bound rests on a stronger inequality that we obtain for arbitrary Schmidt bases and rank, with an optimal constant. Combined with recent results, this yields the unconditional bracket max⁡{−log⁡2(1−4F), M2(ψ~)−4}≤M2NL≤M2(ψ~)\max\{-\log_2(1-4F),\,M_2(\tildeψ)-4\}\le M_2^{\rm NL}\le M_2(\tildeψ)max{−log2​(1−4F),M2​(ψ~​)−4}≤M2NL​≤M2​(ψ~​). We emphasize a structural distinction that makes the non-local quantities the physically preferred diagnostics: whereas the full SRE depends on the (non-unique) encoding of the gauge-invariant local Hilbert space into qubits, the non-local magic, its estimate M2(ψ~)M_2(\tildeψ)M2​(ψ~​), and the anti-flatness are invariant under site-local re-encodings and are therefore intrinsic to the state and bipartition. By varying the gauge coupling for two values of the fermion mass on lattices up to 8×88\times 88×8 (∼288\sim 288∼288 qubits) with bond dimension up to 128128128, we find that the non-local magic, as estimated by M2(ψ~)M_2(\tildeψ)M2​(ψ~​), furnishes a sharper and more bond-dimension-friendly probe of the gauge-matter delocalization crossover compared to the full SRE or the gauge-invariant entanglement entropy, retaining a clear signal at bond dimensions well below those needed to converge the ground state itself.
Recent years have witnessed major progress in the understanding of monitored quantum dynamics, an open quantum setting where the environment is a measurement apparatus that probes the system locally. For the resulting quantum trajectory, unitary evolution and local measurements have competing tendencies in the building of quantum correlations: while the coherent interactions in the former increase the entanglement, the resolving nature of the local measurement collapses the state of the system. Here, the authors study the interplay of monitoring and system dynamics by focusing on the monitored quantum Ising chain as the measurement strength is varied, going from the regime of weak detection, corresponding to the limit of infinite small jumps, to the case of post-selected no-jump case. A sharp transition is found between a logarithmic law phase to an area law phase for the entanglement entropy, which occurs at the same value of the measurement rate in the two limiting situations.
Entanglement phase transitions driven by quantum measurements have emerged as a central paradigm in open quantum many-body physics. Such phase transitions are well established for systems with finite local Hilbert-space dimensions, such as qubits and fermions, while their realization in bosonic systems with unbounded local occupation numbers remains poorly understood. Even in the absence of interactions, number states of bosons are intrinsically non-Gaussian, preventing the use of standard correlation-matrix approaches. To address this problem, we develop a replica-free Keldysh field-theoretic framework that expresses the Renyi entropy of bosonic systems initialized in on-site Fock states in terms of permanents of matrices constructed from single-particle Green's functions. Applying this framework to a continuously monitored one-dimensional cross-stitch lattice conditioned on the no-click trajectory, we uncover a transition from volume-law to logarithmic entanglement scaling. We show that the transition is controlled by a restructuring of the non-Hermitian spectrum that changes the number of long-lived modes from extensive to finite. In the strongly monitored regime, bosons dynamically condense into a microscopic number of slowest-decaying modes, producing logarithmic entanglement scaling, whereas an extensive manifold of long-lived modes at weak monitoring gives rise to volume-law entanglement. Our results establish a distinct mechanism for measurement-induced entanglement transitions in free bosonic systems and provide a computationally efficient diagnostic of the measurement-induced bosonic condensation.