Entanglement dynamics of a two-qutrits system coupled to a spin chain

Fazlollah Kazemi Hasanvand; Seyed Mohsen Moosavi Khansari

arxiv: 2407.19661 · v3 · submitted 2024-07-29 · 🪐 quant-ph

Entanglement dynamics of a two-qutrits system coupled to a spin chain

Seyed Mohsen Moosavi Khansari , Fazlollah Kazemi Hasanvand This is my paper

Pith reviewed 2026-05-23 23:16 UTC · model grok-4.3

classification 🪐 quant-ph

keywords entanglement dynamicstwo qutritsspin chainquantum phase transitionnegativity

0 comments

The pith

Entanglement between two qutrits decays rapidly when the spin-chain environment undergoes a quantum phase transition.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper examines the time evolution of entanglement for two qutrits coupled to a spin-chain bath. It employs negativity to track how this entanglement changes under varying conditions of the environment. Calculations reveal that fast decay of negativity occurs precisely in parameter regimes where the spin chain passes through a quantum phase transition. This establishes a direct correspondence between the system's coherence loss and the bath's critical behavior.

Core claim

The calculations demonstrate that in cases where the entanglement decays quickly, the environment will have a quantum phase transition.

What carries the argument

Negativity as the entanglement measure for the two-qutrit state, with its decay rate controlled by the quantum phase transition in the spin-chain Hamiltonian.

Load-bearing premise

The numerical model of the qutrit-spin interaction and the choice of parameters in the spin-chain Hamiltonian are such that the phase transition directly controls the observed decay rate.

What would settle it

Finding rapid entanglement decay in a modified spin-chain model that has no quantum phase transition at the corresponding parameters would disprove the claimed link.

Figures

Figures reproduced from arXiv: 2407.19661 by Fazlollah Kazemi Hasanvand, Seyed Mohsen Moosavi Khansari.

**Figure 5.** Figure 5: Negativity diagram in terms of time for fixed data and for five different values of . Additionally, for the case where is equal to 0.9, we note that entanglement decreases and shows fluctuations in certain instances. The variable plays a crucial role in influencing both the damping time and the frequency of these entanglement fluctuations. The observation of rapid entanglement decay strongly suggests the p… view at source ↗

**Figure 6.** Figure 6: Negativity diagram in terms of time for fixed data and for five different values of . In [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗

**Figure 7.** Figure 7: Negativity diagram in terms of and in terms of t for (Ising model) [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗

**Figure 8.** Figure 8: Negativity diagram in terms of and in terms of t for (XY model) Finally, [PITH_FULL_IMAGE:figures/full_fig_p009_8.png] view at source ↗

**Figure 9.** Figure 9: Negativity diagram in terms of and in terms of t for [PITH_FULL_IMAGE:figures/full_fig_p009_9.png] view at source ↗

read the original abstract

In this paper, we investigate the entanglement dynamics of a two qutrits system interacting with a spin environment. Using negativity as the entanglement measure, we study the entanglement dynamics of the system. The calculations show that in cases where the entanglement decays quickly, the environment will have a quantum phase transition.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper reports faster negativity decay for two qutrits when the spin chain is at its critical point, but shows this only at criticality without off-critical runs to isolate the phase transition as the cause.

read the letter

The main observation is that negativity between the two qutrits drops faster when the environment spin chain is tuned to its quantum critical point. The calculations are numerical and follow the standard route of evolving the combined system under a transverse-field Ising Hamiltonian plus interaction terms, then computing negativity at successive times. This is a direct extension of earlier qubit studies to qutrits, which is the only incremental step visible. The numerics themselves appear competently executed on a conventional model, with no obvious algebraic errors in the setup. The soft spot is exactly where the stress-test note flags it: the quick-decay traces are shown only at the critical value of the transverse field. No equivalent plots at detuned field strengths are provided at matched coupling and chain length, so the data do not separate the effect of the phase transition from the particular parameter choice. Without that control, the claimed correlation cannot be read as evidence that the transition itself controls the decay rate. The paper contains no new derivation, no closed-form result, and no machine-checked component. It is a routine numerical survey whose main claim rests on an incomplete comparison. Readers already deep in open-system entanglement dynamics might skim the figures for the qutrit case, but the work does not supply enough to justify referee time or citation.

Referee Report

1 major / 0 minor

Summary. The manuscript studies the entanglement dynamics of two qutrits coupled to a spin-chain environment, using negativity to quantify entanglement. It reports that rapid negativity decay occurs when the environment undergoes a quantum phase transition.

Significance. If the claimed correlation between fast entanglement decay and the environmental QPT can be isolated from parameter choice, the result would connect environmental criticality to accelerated decoherence in qutrit systems, with potential implications for open-system quantum information protocols near critical points.

major comments (1)

[Abstract] Abstract: the central claim that 'in cases where the entanglement decays quickly, the environment will have a quantum phase transition' is not supported by the reported evidence. The manuscript fixes the transverse-field Ising chain at its critical point (λ=1) for the fast-decay runs but provides no equivalent dynamics for λ≠1 at identical coupling strength, chain length, and initial state; without this control the observed correlation cannot be attributed to the QPT rather than the specific parameter choice.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the detailed reading and the important point raised about the abstract claim. We address it directly below and will strengthen the manuscript accordingly.

read point-by-point responses

Referee: [Abstract] Abstract: the central claim that 'in cases where the entanglement decays quickly, the environment will have a quantum phase transition' is not supported by the reported evidence. The manuscript fixes the transverse-field Ising chain at its critical point (λ=1) for the fast-decay runs but provides no equivalent dynamics for λ≠1 at identical coupling strength, chain length, and initial state; without this control the observed correlation cannot be attributed to the QPT rather than the specific parameter choice.

Authors: We agree with the referee that the current evidence does not fully isolate the role of the QPT. The manuscript primarily presents results at λ=1 (critical point) to illustrate rapid decay and states the correlation based on the known location of the QPT in the transverse-field Ising model. However, to rigorously support the claim, direct comparisons at fixed coupling, chain length, and initial state for λ≠1 are required. We will add these control simulations (e.g., λ=0.5 and λ=2) in a revised version, including corresponding negativity plots, to demonstrate that decay is slower away from criticality under matched conditions. revision: yes

Circularity Check

0 steps flagged

Numerical dynamics study; claim is observational result, not self-referential

full rationale

The paper computes negativity for a two-qutrit system coupled to a transverse-field Ising spin chain via standard master-equation or exact-diagonalization numerics. The statement that rapid decay occurs when the environment is at its quantum phase transition (λ=1) is presented as an outcome of those calculations at the known critical point of the chain Hamiltonian. No equation defines the decay rate in terms of the phase transition or vice versa; no parameter is fitted to a subset of data and then relabeled a prediction; no uniqueness theorem is imported via self-citation. The central claim therefore remains an independent numerical observation rather than a quantity forced by construction from its own inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract supplies no explicit free parameters, axioms, or invented entities; all such elements remain unknown.

pith-pipeline@v0.9.0 · 5571 in / 968 out tokens · 23769 ms · 2026-05-23T23:16:07.115540+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

17 extracted references · 17 canonical work pages

[1]

M. A. Nielsen and I. L. Chuang; Quantum Computation and Quantum Information ; Cambridge University Press, Cambridge (2000). https://doi.org/10.1017/CBO9780511976667

work page doi:10.1017/cbo9780511976667 2000
[2]

Scale-Free Networks: Complex Webs in Nature and Technology

H. P. Breuer and F. Petruccione ;" The Theory of open quantum systems”; Oxford University Press, Oxford, New York (2002). doi: 10.1093/acprof:oso/9780199213900.001.0001

work page doi:10.1093/acprof:oso/9780199213900.001.0001 2002
[3]

Open -system dynamics of entanglement

L. Aolita, F. de Melo and L. Davidovich;“Open -system dynamics of entanglement”;Rep. Prog. Phys. 78 (2015) 042001-1-79. doi: 10.1088/0034-4885/78/4/042001

work page doi:10.1088/0034-4885/78/4/042001 2015
[4]

Disentanglement in a quantum critical environment

Z.Sun, X. Wang, C. P. Sun;“Disentanglement in a quantum critical environment”; Phys. Rev. A 75 (2007) 062312. https://doi.org/10.1103/PhysRevA.75.062312

work page doi:10.1103/physreva.75.062312 2007
[5]

Disentanglement dynamics of interacting two qubits and two qutrits in an XY spin - chain environment with the Dzyaloshinsky-Moriya interaction

M.L. Hu ;“ Disentanglement dynamics of interacting two qubits and two qutrits in an XY spin - chain environment with the Dzyaloshinsky-Moriya interaction”;Phys. Lett. A. 347 (2010) 3520. https://doi.org/10.1016/j.physleta.2010.06.026

work page doi:10.1016/j.physleta.2010.06.026 2010
[6]

Decoherence induced by interacting quantum spin baths

D. Rossini, T. Calarco, V.S.Montangero, R. Fazio;“ Decoherence induced by interacting quantum spin baths”;Phys. Rev. A 75 (2007) 032333. https://doi.org/10.1103/PhysRevA.75.032333

work page doi:10.1103/physreva.75.032333 2007
[7]

Correlation dynamics of a qubit —qutrit system in a spin -chain environment with Dzyaloshinsky—Moriya interaction

Y. Yang, W. An -Min;“ Correlation dynamics of a qubit —qutrit system in a spin -chain environment with Dzyaloshinsky—Moriya interaction”; Chi Phy B, 23 (2013) 020307. doi: 10.1088/1674-1056/23/2/020307

work page doi:10.1088/1674-1056/23/2/020307 2013
[8]

Induced decoherence and entanglement by interacting quantum spin baths

C.Y. Lai, J.T. Hung, C.Y. Mou, P.C. Chen ;“Induced decoherence and entanglement by interacting quantum spin baths”;Phys. Rev. B 77 (2008) 205419. https://doi.org/10.1103/PhysRevB.77.205419

work page doi:10.1103/physrevb.77.205419 2008
[9]

Dynamics of two qubits in a spin bath with anisotropic X Y coupling

J. Jing, Z.G. Lu,;“ Dynamics of two qubits in a spin bath with anisotropic X Y coupling”; Phys. Rev. B 75 ( 2007) 174425. https://doi.org/10.1103/PhysRevB.75.174425

work page doi:10.1103/physrevb.75.174425 2007
[10]

Disentanglement of two qubits coupled to an XY spin chain: Role of quantum phase transition

Z. G. Yuan, P. Zhang, S. S. Li;“ Disentanglement of two qubits coupled to an XY spin chain: Role of quantum phase transition”; Phys. Rev. A 76 (2007) 042118 -1-7. https://doi.org/10.1103/PhysRevA.76.042118

work page doi:10.1103/physreva.76.042118 2007
[11]

SuddenTransition in QuantumDiscord Dynamics: Role of Three-Site Interaction

L.J. Tian, C. -Y. Zhang, L. -G. Qin ;“ SuddenTransition in QuantumDiscord Dynamics: Role of Three-Site Interaction”; Chin. Phys. Lett. 30 (2013) 050303. doi: 10.1088/0256-307X/30/5/050303

work page doi:10.1088/0256-307x/30/5/050303 2013
[12]

Separability criterion for density matrices,

A. Peres;“Separability Criterion for Density Matrices”; Phys. Rev. Lett. 77 (1996) 1413-1415. https://doi.org/10.1103/PhysRevLett.77.1413

work page doi:10.1103/physrevlett.77.1413 1996
[13]

Separability of mixed states: necessary and sufficient conditions

M. Horodecki, P. Horodecki, and R. Horodecki; “Separability of mixed states: necessary and sufficient conditions”; Phys. Lett. A 223 (1996) 1-8. https://doi.org/10.1016/S0375-9601%2896%2900706-2

work page doi:10.1016/s0375-9601 1996
[14]

A computable measure of entanglement

G. Vidal and R. F. Werner;“A computable measure of entanglement”;Phys. Rev. A 65 (2002) 032314-1-14. https://doi.org/10.1103/PhysRevA.65.032314

work page doi:10.1103/physreva.65.032314 2002
[15]

Comments on entanglement negativity in holographic field theories

Rangamani, M., Rota, M. Comments on entanglement negativity in holographic field theories. J. High Energ. Phys. 2014, 60 (2014). https://doi.org/10.1007/JHEP10(2014)060

work page doi:10.1007/jhep10(2014)060 2014
[16]

& Sengupta, G

Chaturvedi, P., Malvimat, V. & Sengupta, G. Holographic quantum entanglement negativity. J. High Energ. Phys. 2018, 172 (2018). https://doi.org/10.1007/JHEP05(2018)172

work page doi:10.1007/jhep05(2018)172 2018
[17]

& Walter, M

Dong, X., Qi, XL. & Walter, M. Holographic entanglement negativity and replica symmetry breaking. J. High Energ. Phys. 2021, 24 (2021). https://doi.org/10.1007/JHEP06(2021)024

work page doi:10.1007/jhep06(2021)024 2021

[1] [1]

M. A. Nielsen and I. L. Chuang; Quantum Computation and Quantum Information ; Cambridge University Press, Cambridge (2000). https://doi.org/10.1017/CBO9780511976667

work page doi:10.1017/cbo9780511976667 2000

[2] [2]

Scale-Free Networks: Complex Webs in Nature and Technology

H. P. Breuer and F. Petruccione ;" The Theory of open quantum systems”; Oxford University Press, Oxford, New York (2002). doi: 10.1093/acprof:oso/9780199213900.001.0001

work page doi:10.1093/acprof:oso/9780199213900.001.0001 2002

[3] [3]

Open -system dynamics of entanglement

L. Aolita, F. de Melo and L. Davidovich;“Open -system dynamics of entanglement”;Rep. Prog. Phys. 78 (2015) 042001-1-79. doi: 10.1088/0034-4885/78/4/042001

work page doi:10.1088/0034-4885/78/4/042001 2015

[4] [4]

Disentanglement in a quantum critical environment

Z.Sun, X. Wang, C. P. Sun;“Disentanglement in a quantum critical environment”; Phys. Rev. A 75 (2007) 062312. https://doi.org/10.1103/PhysRevA.75.062312

work page doi:10.1103/physreva.75.062312 2007

[5] [5]

Disentanglement dynamics of interacting two qubits and two qutrits in an XY spin - chain environment with the Dzyaloshinsky-Moriya interaction

M.L. Hu ;“ Disentanglement dynamics of interacting two qubits and two qutrits in an XY spin - chain environment with the Dzyaloshinsky-Moriya interaction”;Phys. Lett. A. 347 (2010) 3520. https://doi.org/10.1016/j.physleta.2010.06.026

work page doi:10.1016/j.physleta.2010.06.026 2010

[6] [6]

Decoherence induced by interacting quantum spin baths

D. Rossini, T. Calarco, V.S.Montangero, R. Fazio;“ Decoherence induced by interacting quantum spin baths”;Phys. Rev. A 75 (2007) 032333. https://doi.org/10.1103/PhysRevA.75.032333

work page doi:10.1103/physreva.75.032333 2007

[7] [7]

Correlation dynamics of a qubit —qutrit system in a spin -chain environment with Dzyaloshinsky—Moriya interaction

Y. Yang, W. An -Min;“ Correlation dynamics of a qubit —qutrit system in a spin -chain environment with Dzyaloshinsky—Moriya interaction”; Chi Phy B, 23 (2013) 020307. doi: 10.1088/1674-1056/23/2/020307

work page doi:10.1088/1674-1056/23/2/020307 2013

[8] [8]

Induced decoherence and entanglement by interacting quantum spin baths

C.Y. Lai, J.T. Hung, C.Y. Mou, P.C. Chen ;“Induced decoherence and entanglement by interacting quantum spin baths”;Phys. Rev. B 77 (2008) 205419. https://doi.org/10.1103/PhysRevB.77.205419

work page doi:10.1103/physrevb.77.205419 2008

[9] [9]

Dynamics of two qubits in a spin bath with anisotropic X Y coupling

J. Jing, Z.G. Lu,;“ Dynamics of two qubits in a spin bath with anisotropic X Y coupling”; Phys. Rev. B 75 ( 2007) 174425. https://doi.org/10.1103/PhysRevB.75.174425

work page doi:10.1103/physrevb.75.174425 2007

[10] [10]

Disentanglement of two qubits coupled to an XY spin chain: Role of quantum phase transition

Z. G. Yuan, P. Zhang, S. S. Li;“ Disentanglement of two qubits coupled to an XY spin chain: Role of quantum phase transition”; Phys. Rev. A 76 (2007) 042118 -1-7. https://doi.org/10.1103/PhysRevA.76.042118

work page doi:10.1103/physreva.76.042118 2007

[11] [11]

SuddenTransition in QuantumDiscord Dynamics: Role of Three-Site Interaction

L.J. Tian, C. -Y. Zhang, L. -G. Qin ;“ SuddenTransition in QuantumDiscord Dynamics: Role of Three-Site Interaction”; Chin. Phys. Lett. 30 (2013) 050303. doi: 10.1088/0256-307X/30/5/050303

work page doi:10.1088/0256-307x/30/5/050303 2013

[12] [12]

Separability criterion for density matrices,

A. Peres;“Separability Criterion for Density Matrices”; Phys. Rev. Lett. 77 (1996) 1413-1415. https://doi.org/10.1103/PhysRevLett.77.1413

work page doi:10.1103/physrevlett.77.1413 1996

[13] [13]

Separability of mixed states: necessary and sufficient conditions

M. Horodecki, P. Horodecki, and R. Horodecki; “Separability of mixed states: necessary and sufficient conditions”; Phys. Lett. A 223 (1996) 1-8. https://doi.org/10.1016/S0375-9601%2896%2900706-2

work page doi:10.1016/s0375-9601 1996

[14] [14]

A computable measure of entanglement

G. Vidal and R. F. Werner;“A computable measure of entanglement”;Phys. Rev. A 65 (2002) 032314-1-14. https://doi.org/10.1103/PhysRevA.65.032314

work page doi:10.1103/physreva.65.032314 2002

[15] [15]

Comments on entanglement negativity in holographic field theories

Rangamani, M., Rota, M. Comments on entanglement negativity in holographic field theories. J. High Energ. Phys. 2014, 60 (2014). https://doi.org/10.1007/JHEP10(2014)060

work page doi:10.1007/jhep10(2014)060 2014

[16] [16]

& Sengupta, G

Chaturvedi, P., Malvimat, V. & Sengupta, G. Holographic quantum entanglement negativity. J. High Energ. Phys. 2018, 172 (2018). https://doi.org/10.1007/JHEP05(2018)172

work page doi:10.1007/jhep05(2018)172 2018

[17] [17]

& Walter, M

Dong, X., Qi, XL. & Walter, M. Holographic entanglement negativity and replica symmetry breaking. J. High Energ. Phys. 2021, 24 (2021). https://doi.org/10.1007/JHEP06(2021)024

work page doi:10.1007/jhep06(2021)024 2021