arXiv:2603.03064

Momentum-projected hadron entanglement from lattice-QCD replica correlators

Kiminad A. Mamo

Published Mar 3, 2026• 0 citations

Abstract

We define a finite-volume lattice-QCD observable for the vacuum-subtracted spatial Rényi response of a source--sink-prepared, momentum-projected hadron. At fixed regulator, integer replica index $n>1$, spatial region and gauge-theory cut prescription, double-sided state projection expresses this response as a ratio of replicated and ordinary hadron correlators. The first numerical target is the $n=2$ ratio; its proposed $L^{-3}$ scaling at fixed physical region is to be tested with matched volumes. We implement the measurement in quenched SU(3) for a charged pseudoscalar meson with heavy degenerate Wilson valence quarks, $am_{\rm eff}\simeq2.07$, on two $16^3\times32$ sheets with a central-plaquette cut. Five finite balls and empty/full controls are measured at nine source/sink placements. Their finite-ball means increase with radius at every placement. At the reference placement the three largest responses are 1.6--2.5 times an ideal single-quasiparticle occupancy reference. A full-covariance fit $Δ_{\rm cp}=κ_{\rm occ}S_2^{\rm occ}$ gives $κ_{\rm occ}=1.68\pm0.12$; radius-window and full-control comparisons give values spanning $1.49$--$1.73$. An exact pure-state quark--antiquark pair model interpolates, in the dilute limit, between the unit-occupancy reference ($κ_{\rm occ}=1$) for an unresolved meson and the double-occupancy reference ($κ_{\rm occ}=2$) for a separately resolved quark and antiquark, and yields a boundary-area correction governed by their separation.

DOI: 10.48550/arxiv.2603.03064

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arXiv:2603.03064

Momentum-projected hadron entanglement from lattice-QCD replica correlators

Kiminad A. Mamo

Published Mar 3, 2026• 0 citations

arXiv HTML PDF

Abstract

We define a finite-volume lattice-QCD observable for the vacuum-subtracted spatial Rényi response of a source--sink-prepared, momentum-projected hadron. At fixed regulator, integer replica index

n>1

, spatial region and gauge-theory cut prescription, double-sided state projection expresses this response as a ratio of replicated and ordinary hadron correlators. The first numerical target is the

n=2

ratio; its proposed

L^{-3}

scaling at fixed physical region is to be tested with matched volumes. We implement the measurement in quenched SU(3) for a charged pseudoscalar meson with heavy degenerate Wilson valence quarks,

am_{\rm eff}\simeq2.07

, on two

16^3\times32

sheets with a central-plaquette cut. Five finite balls and empty/full controls are measured at nine source/sink placements. Their finite-ball means increase with radius at every placement. At the reference placement the three largest responses are 1.6--2.5 times an ideal single-quasiparticle occupancy reference. A full-covariance fit

Δ_{\rm cp}=κ_{\rm occ}S_2^{\rm occ}

gives

κ_{\rm occ}=1.68\pm0.12

; radius-window and full-control comparisons give values spanning

1.49

1.73

. An exact pure-state quark--antiquark pair model interpolates, in the dilute limit, between the unit-occupancy reference (

κ_{\rm occ}=1

) for an unresolved meson and the double-occupancy reference (

κ_{\rm occ}=2

) for a separately resolved quark and antiquark, and yields a boundary-area correction governed by their separation.

DOI: 10.48550/arxiv.2603.03064

Related papers

Lattice QCD study of static quark and antiquark correlations via entanglement entropies

TORU T. TAKAHASHI, Yoshiko Kanada-En’yo

We study the color correlation between the static quark and antiquark ( $q\overline{q}$ ) in the confined phase via reduced density matrices $\ensuremath{\rho}$ defined in color space. We adopt the standard Wilson gauge action and perform quenched calculations with the Coulomb gauge condition for reduced density matrices. The spatial volumes are ${L}^{3}={8}^{3}$ , $1{6}^{3}$ , $3{2}^{3}$ , and $4{8}^{3}$ , with the gauge couplings $\ensuremath{\beta}=5.7$, 5.8, and 6.0. Each element of the reduced density matrix in the subspace of quarks' color degrees of freedom of the $q\overline{q}$ pair is calculated from staples defined by link variables. As a result, we find that $\ensuremath{\rho}$ is well written by a linear combination of the strongly correlated $q\overline{q}$ pair state with the color-singlet component and the uncorrelated $q\overline{q}$ pair state with random color configurations. We compute the Renyi entropies ${S}^{\text{Renyi}}$ from $\ensuremath{\rho}$ to investigate the $q\overline{q}$ distance dependence of the color correlation of the $q\overline{q}$ pair and find that the color correlation is quenched as the distance increases.We study the color correlation between the static quark and antiquark ($q\overline{q}$) in the confined phase via reduced density matrices $\ensuremath{\rho}$ defined in color space. We adopt the standard Wilson gauge action and perform quenched calculations with the Coulomb gauge condition for reduced density matrices. The spatial volumes are ${L}^{3}={8}^{3}$, $1{6}^{3}$, $3{2}^{3}$, and $4{8}^{3}$, with the gauge couplings $\ensuremath{\beta}=5.7$, 5.8, and 6.0. Each element of the reduced density matrix in the subspace of quarks' color degrees of freedom of the $q\overline{q}$ pair is calculated from staples defined by link variables. As a result, we find that $\ensuremath{\rho}$ is well written by a linear combination of the strongly correlated $q\overline{q}$ pair state with the color-singlet component and the uncorrelated $q\overline{q}$ pair state with random color configurations. We compute the Renyi entropies ${S}^{\text{Renyi}}$ from $\ensuremath{\rho}$ to investigate the $q\overline{q}$ distance dependence of the color correlation of the $q\overline{q}$ pair and find that the color correlation is quenched as the distance increases.

arXiv:1910.00859Physical review. D/Physical review. D.Dec 4, 20198 citations

Lattice QCD study of static quark and antiquark correlations at finite T via entanglement entropies

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With the aim of clarification of color correlations among quarks, we investigate the color correlation between a static quark and an antiquark (static $q\overline{q}$ ) below and above the phase transition temperature ${T}_{c}$ through the entanglement entropy (EE). By a quenched lattice QCD calculation on an anisotropic lattice adopting the standard Wilson gauge action in the Coulomb gauge, we compute a reduced density matrix $\ensuremath{\rho}$ defined in the color space and the entanglement entropy ${S}_{\mathrm{EE}}$ constructed from $\ensuremath{\rho}$. The spatial volume is ${L}^{3}=2{4}^{3}$ , and the temporal extents are ${N}_{T}=12$ , 13, 14, 15, 16, 18, 20 and 24, with a gauge coupling $\ensuremath{\beta}=5.75$ and a renormalized anisotropy $\ensuremath{\xi}=4.0$, which corresponds to temperatures between 180 and 370 MeV. From an analysis of $\ensuremath{\rho}$ and ${S}_{\mathrm{EE}}$ , the color correlation between $q\overline{q}$ pairs is obtained as a function of the interquark distance $R$ and the temperature $T$ . Below ${T}_{c}$ , the $R$ -dependence of the color correlation resembles that at $T=0$ : the quark's color correlation gradually decreases as $R$ increases due to the color screening by in-between gluons. Above ${T}_{c}$ , due to the deconfinement phase transition, the color correlation among quarks is found to quickly disappear. Further, we investigate the color screening effect via the screening mass defined by $\ensuremath{\rho}$ and discuss the differences in the screening properties between the small and large R regions.With the aim of clarification of color correlations among quarks, we investigate the color correlation between a static quark and an antiquark (static $q\overline{q}$) below and above the phase transition temperature ${T}_{c}$ through the entanglement entropy (EE). By a quenched lattice QCD calculation on an anisotropic lattice adopting the standard Wilson gauge action in the Coulomb gauge, we compute a reduced density matrix $\ensuremath{\rho}$ defined in the color space and the entanglement entropy ${S}_{\mathrm{EE}}$ constructed from $\ensuremath{\rho}$. The spatial volume is ${L}^{3}=2{4}^{3}$, and the temporal extents are ${N}_{T}=12$, 13, 14, 15, 16, 18, 20 and 24, with a gauge coupling $\ensuremath{\beta}=5.75$ and a renormalized anisotropy $\ensuremath{\xi}=4.0$, which corresponds to temperatures between 180 and 370 MeV. From an analysis of $\ensuremath{\rho}$ and ${S}_{\mathrm{EE}}$, the color correlation between $q\overline{q}$ pairs is obtained as a function of the interquark distance $R$ and the temperature $T$. Below ${T}_{c}$, the $R$-dependence of the color correlation resembles that at $T=0$: the quark's color correlation gradually decreases as $R$ increases due to the color screening by in-between gluons. Above ${T}_{c}$, due to the deconfinement phase transition, the color correlation among quarks is found to quickly disappear. Further, we investigate the color screening effect via the screening mass defined by $\ensuremath{\rho}$ and discuss the differences in the screening properties between the small and large R regions.

arXiv:2011.10950Physical review. D/Physical review. D.Feb 11, 20213 citations

Explicit Strong-Coupling Spectral Gaps for SU(2) and SU(3) Lattice Hamiltonians

Bryan W. Daugherty, Gregory Ward, Shawn Ryan

Volume-Uniform Finite-Volume Bounds with the Representation Cutoff Removed: a Reconstruction and Computer-Assisted Improvement of Creation-Operator Constants We study the Kogut–Susskind Hamiltonian of pure SU(2) and SU(3) lattice gauge theory on three-dimensional cubic boxes, H = aΣ_e L_e + bΣ_p (1 - F_p), with L_e the electric Casimir on link e and F_p = N⁻¹Re tr U_p, at strong coupling (small b/a). An unrefereed preprint by Gauvin adapts the creation-operator method of Bravyi, DiVincenzo and Loss to this setting and states, for SU(3), a physical gap uniform in the volume, with the representation cutoff removed, for b/a ≤ 1/648. We give a self-contained reconstruction of the finite-volume argument, identify its external analytic inputs, and reproduce its constants. We then prove a sequence of refinements of the commutator estimate: a selection rule of Wilson-loop multiplication that restricts admissible creation placements, fractional witness counting, orthogonality of output sectors, Haar-measure bounds for vacuum projections before and after the plaquette multiplication, a two-link sandwich identity, a joint vacuum-row bound, and a size-weighted norm. The finite tuple constants and final sufficient inequalities are checked in exact rational arithmetic by two author implementations and a separate verifier written from the stated definitions. The operator inequalities that justify these arithmetic definitions are proved analytically. On open boxes the physical gap is at least 3a/2 for SU(2) whenever b/a ≤ 2/95, and at least 8a/3 for SU(3) whenever b/a ≤ 2/35 (1/16 with a sharper representation-theoretic bound), uniformly in the box. These sufficient couplings are 3072/95 and 1296/35 times those obtained from the preprint's constants (for SU(2), our transfer of them). The corresponding open-box endpoints in Hamiltonian units are β_H=√(4/95) ≈ 0.205 for SU(2) and β_H=√(6/35) ≈ 0.414 for SU(3), or √(3/16) ≈ 0.433 with the strengthened SU(3) bound. The basic open-box certificates also bound the static fundamental potential below linearly: for static charges at graph distance L ≥ 6, E_{x,y} - E_vac ≥ σ L with σ = 5/16 a for SU(2) at b/a ≤ 2/95 and σ = 5/9 a for SU(3) at b/a ≤ 2/35, uniformly in the box. A variable exclusion fraction and an independent local-decoupling upper bound bracket the first physical excitation energy above the vacuum. On open boxes containing an elementary plaquette, at b/a = 1/5000 this energy lies in [2.990, 3.050] a (SU(2)) and [5.326, 5.390] a (SU(3)). These are strong-coupling statements at fixed lattice spacing, not continuum statements. Files ym_strong_coupling_gaps.pdf: the paper. zenodo_ymgap_v1.0.0_2026-10-23.zip: the certificate bundle: two independent implementations of the certified tuple constants, the verifier, the tamper-test driver, the Section 8 upper-bound program and its exact checker, the number generator, manifests and verifier outputs for all 34 certificate configurations, the complete tuple files, and the paper source with every number generated from these files. Its SHA-256 is in the adjacent .sha256 file; SHA256SUMS inside covers every file. README.md, LICENSE.md: copies of the bundle's front matter. Verification ./replay.sh (Python 3, standard library only; a few minutes) regenerates every tuple file, compares it entry by entry with the second implementation, verifies every manifest in exact rational arithmetic, runs the tamper tests and the exact check of the two-sided bracket upper bounds, and regenerates every number of the paper; it exits non-zero on any failure. Scope: strong-coupling statements for the Kogut–Susskind lattice Hamiltonian at fixed lattice spacing, uniform in the volume, with the representation cutoff removed. They are not continuum statements and do not address the continuum Yang–Mills mass gap problem. Licence: CC BY-NC 4.0 (LICENSE.md), licensed by SmartLedger Solutions. Commercial-use enquiries: labs@smartledger.solutions. No patent licence is granted by this release.Volume-Uniform Finite-Volume Bounds with the Representation Cutoff Removed: a Reconstruction and Computer-Assisted Improvement of Creation-Operator Constants We study the Kogut–Susskind Hamiltonian of pure SU(2) and SU(3) lattice gauge theory on three-dimensional cubic boxes, H = aΣ_e L_e + bΣ_p (1 - F_p), with L_e the electric Casimir on link e and F_p = N⁻¹Re tr U_p, at strong coupling (small b/a). An unrefereed preprint by Gauvin adapts the creation-operator method of Bravyi, DiVincenzo and Loss to this setting and states, for SU(3), a physical gap uniform in the volume, with the representation cutoff removed, for b/a ≤ 1/648. We give a self-contained reconstruction of the finite-volume argument, identify its external analytic inputs, and reproduce its constants. We then prove a sequence of refinements of the commutator estimate: a selection rule of Wilson-loop multiplication that restricts admissible creation placements, fractional witness counting, orthogonality of output sectors, Haar-measure bounds for vacuum projections before and after the plaquette multiplication, a two-link sandwich identity, a joint vacuum-row bound, and a size-weighted norm. The finite tuple constants and final sufficient inequalities are checked in exact rational arithmetic by two author implementations and a separate verifier written from the stated definitions. The operator inequalities that justify these arithmetic definitions are proved analytically. On open boxes the physical gap is at least 3a/2 for SU(2) whenever b/a ≤ 2/95, and at least 8a/3 for SU(3) whenever b/a ≤ 2/35 (1/16 with a sharper representation-theoretic bound), uniformly in the box. These sufficient couplings are 3072/95 and 1296/35 times those obtained from the preprint's constants (for SU(2), our transfer of them). The corresponding open-box endpoints in Hamiltonian units are β_H=√(4/95) ≈ 0.205 for SU(2) and β_H=√(6/35) ≈ 0.414 for SU(3), or √(3/16) ≈ 0.433 with the strengthened SU(3) bound. The basic open-box certificates also bound the static fundamental potential below linearly: for static charges at graph distance L ≥ 6, E_{x,y} - E_vac ≥ σ L with σ = 5/16 a for SU(2) at b/a ≤ 2/95 and σ = 5/9 a for SU(3) at b/a ≤ 2/35, uniformly in the box. A variable exclusion fraction and an independent local-decoupling upper bound bracket the first physical excitation energy above the vacuum. On open boxes containing an elementary plaquette, at b/a = 1/5000 this energy lies in [2.990, 3.050] a (SU(2)) and [5.326, 5.390] a (SU(3)). These are strong-coupling statements at fixed lattice spacing, not continuum statements. Files ym_strong_coupling_gaps.pdf: the paper. zenodo_ymgap_v1.0.0_2026-10-23.zip: the certificate bundle: two independent implementations of the certified tuple constants, the verifier, the tamper-test driver, the Section 8 upper-bound program and its exact checker, the number generator, manifests and verifier outputs for all 34 certificate configurations, the complete tuple files, and the paper source with every number generated from these files. Its SHA-256 is in the adjacent .sha256 file; SHA256SUMS inside covers every file. README.md, LICENSE.md: copies of the bundle's front matter. Verification ./replay.sh (Python 3, standard library only; a few minutes) regenerates every tuple file, compares it entry by entry with the second implementation, verifies every manifest in exact rational arithmetic, runs the tamper tests and the exact check of the two-sided bracket upper bounds, and regenerates every number of the paper; it exits non-zero on any failure. Scope: strong-coupling statements for the Kogut–Susskind lattice Hamiltonian at fixed lattice spacing, uniform in the volume, with the representation cutoff removed. They are not continuum statements and do not address the continuum Yang–Mills mass gap problem. Licence: CC BY-NC 4.0 (LICENSE.md), licensed by SmartLedger Solutions. Commercial-use enquiries: labs@smartledger.solutions. No patent licence is granted by this release.

Oct 23, 20260 citations

Quantum computation of hadron scattering in a lattice gauge theory

Zohreh Davoudi, Chung-Chun Hsieh, Saurabh V. Kadam

We present a digital quantum computation of two-hadron scattering in a $Z_2$ lattice gauge theory in 1+1 dimensions. We prepare well-separated single-particle wave packets with desired momentum-space wavefunctions, and simulate their collision through digitized time evolution. Multiple hadronic wave packets can be produced using the efficient, systematically improvable algorithm of this work, achieving high fidelity with the target initial state. Specifically, employing a trapped-ion quantum computer (IonQ Forte), we prepare up to three meson wave packets using 11 and 27 system qubits, and simulate collision dynamics of two meson wave packets for the smaller system. Results for local observables are consistent with numerical simulations at early times, but decoherence effects limit evolution into long times. We demonstrate the critical role of high-fidelity initial states for precision measurements of state-sensitive observables, such as $S$ -matrix elements. Our work establishes the potential of quantum computers in simulating hadron-scattering processes in strongly interacting gauge theories.We present a digital quantum computation of two-hadron scattering in a $Z_2$ lattice gauge theory in 1+1 dimensions. We prepare well-separated single-particle wave packets with desired momentum-space wavefunctions, and simulate their collision through digitized time evolution. Multiple hadronic wave packets can be produced using the efficient, systematically improvable algorithm of this work, achieving high fidelity with the target initial state. Specifically, employing a trapped-ion quantum computer (IonQ Forte), we prepare up to three meson wave packets using 11 and 27 system qubits, and simulate collision dynamics of two meson wave packets for the smaller system. Results for local observables are consistent with numerical simulations at early times, but decoherence effects limit evolution into long times. We demonstrate the critical role of high-fidelity initial states for precision measurements of state-sensitive observables, such as $S$-matrix elements. Our work establishes the potential of quantum computers in simulating hadron-scattering processes in strongly interacting gauge theories.

arXiv:2505.20408May 26, 20251 citation

Improved lattice method for determining entanglement measures in SU(N) gauge theories

Tobias Rindlisbacher, Niko Jokela, Arttu Pönni +2 more

The determination of entanglement measures in SU(N) gauge theories is a non-trivial task. With the so-called "replica trick", a family of entanglement measures, known as "Rényi entropies", can be determined with lattice Monte Carlo. Unfortunately, the standard implementation of the replica method for SU(N) lattice gauge theories suffers from a severe signal-to-noise ratio problem, rendering high-precision studies of Rényi entropies prohibitively expensive. In this work, we propose a method to overcome the signal-to-noise ratio problem and show some first results for SU(N) in 4 dimensions.The determination of entanglement measures in SU(N) gauge theories is a non-trivial task. With the so-called "replica trick", a family of entanglement measures, known as "Rényi entropies", can be determined with lattice Monte Carlo. Unfortunately, the standard implementation of the replica method for SU(N) lattice gauge theories suffers from a severe signal-to-noise ratio problem, rendering high-precision studies of Rényi entropies prohibitively expensive. In this work, we propose a method to overcome the signal-to-noise ratio problem and show some first results for SU(N) in 4 dimensions.

International Symposium on Lattice Field Theory (LATTICE)Nov 7, 20229 citations

Exact twist-field correlators of the Yang–Lee minimal model on the lattice: two critical realizations and a three-level test

Rongzhen Dai

The Rényi entropies of a non-unitary critical system are not fixed by a single power of the central charge but by the full four-point function of twist fields in a cyclic orbifold, constrained by null-vector equations. For the Yang–Lee universality class—the minimal model with —Dupic, Estienne and Ikhlef (DEI) computed several of these twist correlators in closed form. We provide an independent lattice realization and calibration of those exact correlators on two distinct critical lattice models: the critical Restricted Solid-On-Solid (RSOS) model with and the quantum Ising chain in an imaginary longitudinal field. Both are diagonalised exactly, and the lattice-to-continuum correspondence is certified on three independent objects: the low-lying spectrum reproduces the tower with effective central charge and no exceptional-point degeneracy on the RSOS side; the single-interval vacuum and ground-state twist correlators reproduce the exact two- and four-point functions, including a quantitative determination of the sub-leading fusion channel; and the vacuum two-interval four-twist function is reproduced with a crossing self-consistency of . Along the way we correct a typographical error in the DEI Temperley–Lieb Hamiltonian. We define precisely the boundary-height-sector-resolved trace functional that the lattice certifies, and we do not address the microscopic-realization dependence of the physical two-interval mutual information, which involves a choice of observable subalgebra and is left to a separate study.The Rényi entropies of a non-unitary critical system are not fixed by a single power of the central charge but by the full four-point function of twist fields in a cyclic orbifold, constrained by null-vector equations. For the Yang–Lee universality class—the minimal model with —Dupic, Estienne and Ikhlef (DEI) computed several of these twist correlators in closed form. We provide an independent lattice realization and calibration of those exact correlators on two distinct critical lattice models: the critical Restricted Solid-On-Solid (RSOS) model with and the quantum Ising chain in an imaginary longitudinal field. Both are diagonalised exactly, and the lattice-to-continuum correspondence is certified on three independent objects: the low-lying spectrum reproduces the tower with effective central charge and no exceptional-point degeneracy on the RSOS side; the single-interval vacuum and ground-state twist correlators reproduce the exact two- and four-point functions, including a quantitative determination of the sub-leading fusion channel; and the vacuum two-interval four-twist function is reproduced with a crossing self-consistency of . Along the way we correct a typographical error in the DEI Temperley–Lieb Hamiltonian. We define precisely the boundary-height-sector-resolved trace functional that the lattice certifies, and we do not address the microscopic-realization dependence of the physical two-interval mutual information, which involves a choice of observable subalgebra and is left to a separate study.

Jul 24, 20260 citations

We define a finite-volume lattice-QCD observable for the vacuum-subtracted spatial Rényi response of a source--sink-prepared, momentum-projected hadron. At fixed regulator, integer replica index

n>1

, spatial region and gauge-theory cut prescription, double-sided state projection expresses this response as a ratio of replicated and ordinary hadron correlators. The first numerical target is the

n=2

ratio; its proposed

L^{-3}

scaling at fixed physical region is to be tested with matched volumes. We implement the measurement in quenched SU(3) for a charged pseudoscalar meson with heavy degenerate Wilson valence quarks,

am_{\rm eff}\simeq2.07

, on two

16^3\times32

Δ_{\rm cp}=κ_{\rm occ}S_2^{\rm occ}

gives

κ_{\rm occ}=1.68\pm0.12

; radius-window and full-control comparisons give values spanning

1.49

1.73

. An exact pure-state quark--antiquark pair model interpolates, in the dilute limit, between the unit-occupancy reference (

κ_{\rm occ}=1

) for an unresolved meson and the double-occupancy reference (

κ_{\rm occ}=2

) for a separately resolved quark and antiquark, and yields a boundary-area correction governed by their separation.

We study the color correlation between the static quark and antiquark (

q\overline{q}

) in the confined phase via reduced density matrices $\ensuremath{\rho}$ defined in color space. We adopt the standard Wilson gauge action and perform quenched calculations with the Coulomb gauge condition for reduced density matrices. The spatial volumes are

{L}^{3}={8}^{3}

1{6}^{3}

3{2}^{3}

, and

4{8}^{3}

, with the gauge couplings $\ensuremath{\beta}=5.7$, 5.8, and 6.0. Each element of the reduced density matrix in the subspace of quarks' color degrees of freedom of the

q\overline{q}

pair is calculated from staples defined by link variables. As a result, we find that $\ensuremath{\rho}$ is well written by a linear combination of the strongly correlated

q\overline{q}

pair state with the color-singlet component and the uncorrelated

q\overline{q}

pair state with random color configurations. We compute the Renyi entropies

{S}^{\text{Renyi}}

from $\ensuremath{\rho}$ to investigate the

q\overline{q}

distance dependence of the color correlation of the

q\overline{q}

pair and find that the color correlation is quenched as the distance increases.

With the aim of clarification of color correlations among quarks, we investigate the color correlation between a static quark and an antiquark (static

q\overline{q}

) below and above the phase transition temperature

{T}_{c}

through the entanglement entropy (EE). By a quenched lattice QCD calculation on an anisotropic lattice adopting the standard Wilson gauge action in the Coulomb gauge, we compute a reduced density matrix $\ensuremath{\rho}$ defined in the color space and the entanglement entropy

{S}_{\mathrm{EE}}

constructed from $\ensuremath{\rho}$. The spatial volume is

{L}^{3}=2{4}^{3}

, and the temporal extents are

{N}_{T}=12

, 13, 14, 15, 16, 18, 20 and 24, with a gauge coupling $\ensuremath{\beta}=5.75$ and a renormalized anisotropy $\ensuremath{\xi}=4.0$, which corresponds to temperatures between 180 and 370 MeV. From an analysis of $\ensuremath{\rho}$ and

{S}_{\mathrm{EE}}

, the color correlation between

q\overline{q}

pairs is obtained as a function of the interquark distance

R

and the temperature

T

. Below

{T}_{c}

, the

R

-dependence of the color correlation resembles that at

T=0

: the quark's color correlation gradually decreases as

R

increases due to the color screening by in-between gluons. Above

{T}_{c}

, due to the deconfinement phase transition, the color correlation among quarks is found to quickly disappear. Further, we investigate the color screening effect via the screening mass defined by $\ensuremath{\rho}$ and discuss the differences in the screening properties between the small and large R regions.

We present a digital quantum computation of two-hadron scattering in a

Z_2

lattice gauge theory in 1+1 dimensions. We prepare well-separated single-particle wave packets with desired momentum-space wavefunctions, and simulate their collision through digitized time evolution. Multiple hadronic wave packets can be produced using the efficient, systematically improvable algorithm of this work, achieving high fidelity with the target initial state. Specifically, employing a trapped-ion quantum computer (IonQ Forte), we prepare up to three meson wave packets using 11 and 27 system qubits, and simulate collision dynamics of two meson wave packets for the smaller system. Results for local observables are consistent with numerical simulations at early times, but decoherence effects limit evolution into long times. We demonstrate the critical role of high-fidelity initial states for precision measurements of state-sensitive observables, such as

S

-matrix elements. Our work establishes the potential of quantum computers in simulating hadron-scattering processes in strongly interacting gauge theories.