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Comparative analysis of robust entanglement generation in engineered XX spin chains

T0 review · 3 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read The paper claims that a dual-port boundary-field protocol (P2) consistently beats a staggered-coupling protocol (P1) at generating end-to-end entanglement in XX spin chains, across spin values $s = 1/2, 1, 3/2$, and that P2 keeps its…

desk verdict Useful comparative numerics on spin-chain entanglement generation, but the dual-port protocol's robustness edge may be an artifact of an asymmetric benchmark. read the letter →

arxiv 2505.22484 v2 pith:XOONP3JA submitted 2025-05-28 quant-ph math-phmath.MP

Eduardo K. Soares , Gentil D. de Moraes Neto , Fabiano M. Andrade This is my paper
classification quant-phmath-phmath.MP
keywords quantumspinchainsentanglementgenerationXXmodelnegativitydephasingdisordernon-Markoviandynamicspseudomodeformalism
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper compares two ways to generate entanglement between the ends of a finite XX spin chain. Protocol 1 steers real excitations through the chain using alternating strong and weak couplings, while Protocol 2 applies optimized magnetic fields only at the boundary spins, so the bulk stays virtually unexcited. Across spin values $s = 1/2$, $1$, and $3/2$, the dual-port protocol reaches higher end-to-end negativity in shorter times under identical system parameters, and it retains more entanglement under disorder, dephasing, and non-Markovian reservoirs. If correct, this makes dual-port boundary control a practical route to fast, on-demand entanglement distribution in solid-state quantum devices.

What carries the argument

The load-bearing object is the dual-port architecture of P2 together with the effective dispersive Hamiltonian that describes it. A uniform chain with couplings $\Delta$ and weak boundary couplings $\delta$, plus optimized boundary fields $B$, maps via a fermionization mapping to non-interacting fermions in the single-excitation subspace; in the dispersive regime $\lambda_k/\zeta_k \ll 1$, second-order perturbation theory yields an effective direct coupling $\mathcal{H}_{\rm eff} = \chi(S_e^+ S_r^- + S_e^- S_r^+)$ with $\chi = \sum_k \lambda_k^2/\zeta_k$. This effective coupling produces entanglement through virtual, not real, bulk excitations, with average bulk population $\langle n \rangle \approx N(\pi\delta/2\Delta)^2$ and a renormalized dephasing rate $\Gamma \propto \gamma(\lambda/J)^2$. P1 lacks this effective decoupling: its staggered couplings require physical propagation through the bulk, so each populated intermediate site contributes to noise accumulation.

What would settle it

Measure the maximum bulk population during P2 evolution in a seven-site chain; the virtual-excitation explanation predicts $\langle n \rangle \approx N(\pi\delta/2\Delta)^2$, so an observed population orders of magnitude larger would contradict the mechanism. Alternatively, rerun the benchmark with $B$ fixed to the same value for all spin values and chain lengths; if P1 then matches or beats P2 at any $s$, the uniform-outperformance claim fails.

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Extended reading notes

Core claim

The paper's central claim is that Protocol 2 (P2), which uses optimized boundary magnetic fields to mediate virtual excitations between terminal spins, consistently outperforms Protocol 1 (P1), which relies on staggered couplings to steer real excitations along the chain. For a seven-site chain at dimerization ratio $\Delta/\delta = 10$, P2 reaches normalized end-to-end negativity $1.0$ at $t = 13\delta$ for $s = 1/2$, while P1 reaches $1.0$ only at $t = 22.5\delta$; for $s = 1$ the peaks are $0.94$ versus $0.75$, and for $s = 3/2$ they are $0.90$ versus $0.62$. P2 also requires only re-optimizing a single boundary-field value when the chain length changes, and under diagonal and off-diagonal disorder, dephasing, and Lorentzian non-Markovian reservoirs it maintains higher peak negativity over a wider parameter region. The authors attribute this to suppression of bulk population: the intermediate spins remain virtually unexcited, so bulk disorder, dephasing, and environment-induced backflow couple only weakly to the entangled pair.

Load-bearing premise

The comparison assumes P2's boundary magnetic field may be tuned separately for each chain length and spin value to maximize the reported entanglement, while P1 is not given any comparable tuning; if both protocols were optimized on equal footing, or if the field had to be chosen before the target parameters were known, the claimed advantage could shrink or disappear.

Editorial extensions

If this is right

  • For spin-$1/2$ chains of length $N = 7$, P2 produces the Bell state in about $13\delta$ compared with P1's $22.5\delta$, so entanglement can be distributed on a shorter timescale under identical coupling parameters.
  • P2 keeps working in higher-spin chains where P1 degrades (peaks $0.94$ versus $0.75$ for $s = 1$ and $0.90$ versus $0.62$ for $s = 3/2$), extending the scheme beyond qubits to higher-dimensional spin channels.
  • Because P2 tolerates diagonal and off-diagonal disorder up to $E \approx 0.75\delta$ with substantial entanglement, it relaxes fabrication precision requirements for solid-state implementations.
  • P2's flat negativity decay under dephasing and its broad high-entanglement region under non-Markovian reservoirs suggest it suits platforms where local noise and environmental memory are unavoidable.
  • The protocol scales to arbitrary $N$ for $s = 1/2$ by re-optimizing a single boundary field $B$, so extending to longer chains does not require redesigning the whole coupling pattern.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The paper does not test whether P1 could match P2 if its coupling pattern were co-optimized with weak boundary fields; a control-optimized head-to-head benchmark would sharpen the comparison.
  • P2's robustness rests on keeping the bulk dark, so one would expect it to also suppress noise channels that act only on the bulk, such as correlated low-frequency flux noise, even though the paper only simulates Lorentzian reservoirs.
  • The same virtual-excitation mechanism should generalize to layouts with more than two ports, such as a central hub coupling several boundary qubits, but the paper does not simulate multi-receiver entanglement.
  • A practical open question is whether a single fixed boundary field $B$ can serve all chain lengths and spin values; the paper optimizes $B$ per instance, so robustness under fixed control settings remains untested.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The manuscript numerically compares two protocols for generating entanglement between the ends of an XX spin chain with spin magnitudes s = 1/2, 1, and 3/2: Protocol 1 (P1) uses staggered couplings with no boundary fields, while Protocol 2 (P2) uses a dual-port architecture with optimized boundary magnetic fields. The authors report that P2 reaches higher end-to-end negativity in shorter times and is more robust to diagonal and off-diagonal static disorder, dephasing, and non-Markovian reservoirs. An effective dispersive Hamiltonian (Appendix A) is used to explain P2's low bulk population and suppressed dephasing rate.

Significance. If validated, the dual-port scheme would offer a practical route to fast, robust entanglement generation in spin-chain implementations. The paper's main strengths are the systematic numerical survey across spin values and noise models and the independent effective-model derivation in Appendix A, which connects the observed robustness to a concrete physical mechanism (virtual, rather than real, bulk excitation). However, the headline superiority claim is currently supported by an asymmetric comparison: P2's boundary field is optimized per instance whereas P1 is not optimized, and the diagonal-disorder model applies a perturbation that is relatively small for P2 but large for P1. These issues need to be addressed before the central claim is fully established.

major comments (3)
  1. [Section 3.1, Table 1, Figure 4] The central quantitative comparison is not symmetric. P2's boundary magnetic field B is optimized separately for each spin value (B = 3.7, 2.9, 4.7 in Table 1) and for each chain length (Figure 4), while P1 is evolved with B_i = 0 and no comparable parameter optimization. The abstract's phrase 'under the same system parameters' is therefore misleading, because the protocols have different boundary fields and P2 has an extra tunable parameter. To support the claim of superior speed and fidelity, the authors should either optimize P1 over its natural parameters (e.g., the dimerization ratio Δ/δ or boundary fields) or evaluate P2 with a fixed, non-optimized B, and demonstrate that the advantage remains.
  2. [Section 3.2, Eq. (7), Figure 5] The diagonal-disorder model is inequitable between the two protocols. Equation (7) adds random local fields only at sites 1 and N-1. For P2, these fields are small perturbations on top of the optimized boundary field B ≈ 3.7δ, whereas for P1, which has zero baseline field, the same absolute perturbation introduces a Zeeman energy of order Eδ that can be comparable to the coupling δ and substantially detunes the boundary sites. The faster degradation of P1 in Figure 5 may therefore be caused by an unfavorable perturbation scale rather than an intrinsic sensitivity to on-site disorder. Please apply diagonal disorder to all sites (or at least to the terminal spins) for both protocols, or scale the disorder by the local field amplitude, and re-examine the robustness comparison.
  3. [Section 3.3, Figure 8, Appendix A] The interpretation of the dephasing results would be strengthened by a quantitative check of the effective model. The inset of Figure 8 and Eq. (12) explain that P2's dephasing resilience comes from a renormalized rate Γ ∝ γ(λ/J)^2 and low bulk population. Since this effective model assumes the dispersive regime and relies on the optimized boundary field, a direct comparison of the effective-model prediction with the full numerics for the same parameters (e.g., the slope of the negativity decay at small γ) would make the reasoning more convincing. As written, the connection is qualitative only.
minor comments (5)
  1. [Section 2, Eq. (3)] The negativity formula should be written as N(ρ) = (||ρ^{T_A}||_1 − 1)/2; the current typesetting '||ρ^{T_A}||_1 − 1 / 2' is ambiguous.
  2. [Section 3.1, Table 1] The times in Table 1 are given 'in units of δ' but the caption should clarify that these are dimensionless products t·δ, so that the reader knows the actual energy/frequency scale.
  3. [Section 3.4] The system–reservoir coupling operator L = Σ_i (S^z_i + S^x_i) in the pseudomode calculation is introduced without justification; please specify which physical noise mechanisms this operator models for each protocol.
  4. [Appendix A.2] The derivation of the trimer coupling η in Eq. (A12) is not shown; please add a few intermediate steps or a reference.
  5. [Data Availability] The data availability statement says data are available upon reasonable request; for a numerical study of this type, depositing the simulation code would improve reproducibility.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the comparative results are produced by direct numerical integration of the XX Hamiltonian, and the optimized boundary field B is a protocol control parameter rather than a fitted input renamed as a prediction.

full rationale

The paper's central claims are generated by solving Eq. (1) and Eq. (2) numerically with QuTiP; the effective Hamiltonians in Appendix A are explicitly presented as explanatory approximations, and the text states that "our main conclusions are based entirely on the numerical data." The optimized boundary field B in P2 is a control parameter of the protocol, not a parameter fitted to the same quantity it is used to predict: the reported negativities are obtained by sweeping B and taking the best value, which is standard protocol benchmarking rather than a self-referential derivation. The self-citation [35] motivates P2 but is not load-bearing, because P2's dynamics are independently simulated from the Hamiltonian in this work and no uniqueness or existence claim is imported from it. The main weakness is comparison fairness: P2 is run at its optimized B while P1 is run at B=0, so the claim of "same system parameters" is not strictly accurate, and the disorder comparison in Eq. (7) adds diagonal noise only at the boundary sites, which can affect the two protocols asymmetrically. However, this is a benchmarking or correctness concern, not a circularity: no equation is defined in terms of the outcome it is used to explain, and no reported prediction is equivalent by construction to an input. Accordingly, no circular step can be quoted.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

The central claim depends on the XX model, the Lindblad and pseudomode open-system treatments, and the boundary-field optimization for P2. No new particles or forces are introduced. The main free parameter is the optimized boundary field B, which is tuned per instance to the target figure of merit.

free parameters (2)
  • Boundary magnetic field B for P2 = 3.7, 2.9, 4.7 (units of δ) for s=1/2, 1, 3/2 (N=7); optimized per N in Figure 4
    P2's entanglement peak is maximized by numerical search over B for each spin value and chain length, and the reported P2 advantage is evaluated at these optimized values (Section 3.1, Table 1, Figure 4).
  • Dimerization ratio Δ/δ = 10 in the main text; 30 in Figure 8
    Chosen by hand to operate in the strong-dimerization or dispersive regime; not derived from an experimental constraint or benchmark.
assumptions (5)
  • domain assumption The alternating-coupling XX Hamiltonian (Eq. 1) is a valid model for engineered spin-chain entanglement platforms.
    Used throughout; the concluding section lists candidate physical implementations but no microscopic derivation is given.
  • domain assumption The Lindblad master equation with local Sz dephasing (Eq. 2) captures Markovian decoherence in the dephasing analysis.
    Assumed in Section 2 and used for Figure 8; the authors supplement it with pseudomode non-Markovian dynamics.
  • standard math The Lorentzian pseudomode mapping (Eqs. 15-17) gives exact reduced dynamics for the chosen reservoir, with L = Σ_i(S_z^i + S_x^i).
    Taken from Refs. [41,42]; the choice of L is a modeling assumption for simultaneous dephasing and dissipation.
  • standard math Second-order perturbation theory in the dispersive limit (λ_k/ζ_k << 1) yields the effective two-qubit Hamiltonian (Eq. 10).
    Used to explain P2's dephasing robustness; for N=7 and Δ/δ=10 the stated validity condition N << ζ_k/λ_k is only marginally satisfied (Appendix A.1).
  • domain assumption Higher-spin computational basis states are identified with Sz eigenstates as described in Section 2.
    The normalization of negativity and the definition of target states for s=1 and 3/2 depend on this convention.

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Pith. "Pith review of Comparative analysis of robust entanglement generation in engineered XX spin chains." pith.science (2026). https://pith.science/paper/XOONP3JA

@misc{pith2026250522484,
  author       = {Pith},
  title        = {Pith review of: Comparative analysis of robust entanglement generation in engineered XX spin chains},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XOONP3JA}},
  note         = {Machine review of arXiv:2505.22484}
}
abstract

We present a numerical investigation comparing two entanglement generation protocols in finite XX spin chains with varying spin magnitudes ($s = 1/2, 1, 3/2 $). Protocol 1 (P1) relies on staggered couplings to steer correlations toward the ends of the chain. At the same time, Protocol 2 (P2) adopts a dual-port architecture that uses optimized boundary fields to mediate virtual excitations between terminal spins. Our results show that P2 consistently outperforms P1 in all spin values, generating higher-fidelity entanglement in shorter timescales when evaluated under the same system parameters. Furthermore, P2 exhibits superior robustness under realistic imperfections, including diagonal and off-diagonal disorder, as well as dephasing noise. These advantages stem from its ability to suppress the bulk population and minimize susceptibility to decoherence. Together, the scalability, efficiency, and noise resilience of the dual-port approach position it as a promising framework for entanglement distribution in solid-state quantum information platforms.

Figures

Figures reproduced from arXiv: 2505.22484 by the authors.

Figure 1
Figure 1. (a) P1 and (b) P2 architectures. Bold lines represent ∆ couplings, while thin lines indicate δ couplings. The system evolves under the Lindblad master equation [51–53], which describes the combined unitary and dissipative dynamics: ρ˙ = −i[H, ρ] + γ N ∑ i=1  S z i ρS z i − 1 2 S z i S z i , ρ  . (2) The dissipative term proportional to γ introduces local pure dephasing, a common and critical source of decoherence … view at source ↗
Figure 2
Figure 2. Time evolution of the end-to-end negativity for (a) s = 1/2, (b) s = 1, and (c) s = 3/2. All traces correspond to the same dimerization ratio ∆/δ = 10. Results are shown for P1 (red curves) and P2 (blue curves). P2 can also be extended to arbitrary chain lengths N when s = 1/2, making it possible to obtain maximally entangled states for higher values of N. For each system size, we only need to optimize the boundary … view at source ↗
Figure 3
Figure 3. Time evolution of fidelity when considering [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: Contour plot of negativity values as a function of time and the magnetic field applied to the boundaries for a N = 7 chain. We set the dimerization ratio to ∆/δ = 10. 3.2. Robustness of the Spin-1/2 Protocol The performance advantage of P2 is most relevant when it surv…
Figure 5
Figure 5. Figure 5: shows that P2 maintains excellent performance even at high disorder strengths, while P1 suffers significant entanglement degradation. This robustness is particularly valuable for practical implementations, as it allows for high entanglement generation (high negativity …
Figure 6
Figure 6. Figure 6: Average peak negativity as function of off-diagonal disorder strength E. The red line represents P1, while P2 is shown as a blue line. The red and blue bars indicate the standard deviation from the mean for each protocol. We set the dimerization ratio to ∆/δ = 10 [PIT…
Figure 7
Figure 7. Figure 7: Average peak negativity as function of combined diagonal and off-diagonal disorder strength E. The red line represents P1, while P2 is shown as a blue line. The red and blue bars indicate the standard deviation from the mean for each protocol. We set the dimerization r…
Figure 8
Figure 8. Figure 8: Peak end-to-end negativity as function of boundary dephasing rate γ, shown for two coupling regimes: ∆ = 10 and ∆ = 30, with δ = 1. The main plot compares the performance of protocols P1 and P2, highlighting the enhanced robustness of P2, which exhibits a slower decay …
Figure 9
Figure 9. Figure 9: Maximum normalized end-to-end negativity achieved within an evolution time equal to twice the optimal transfer time of the closed system, for both protocols under non-Markovian dissipation modeled via the pseudomode method. Each column corresponds to a different spectr…

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Works this paper leans on

93 extracted references · 36 canonical work pages

  1. [1]

    The quantum technologies roadmap: A European community view

    Acín, A.; Bloch, I.; Buhrman, H.; Calarco, T.; Eichler, C.; Eisert, J.; Esteve, D.; Gisin, N.; Glaser, S.J.; Jelezko, F.; et al. The quantum technologies roadmap: A European community view. New J. Phys. 2018, 20, 080201. https://doi.org/10.1088/1367-2630/aad1ea

    doi:10.1088/1367-2630/aad1ea 2018

  2. [2]

    Quantum resource theories

    Chitambar, E.; Gour, G. Quantum resource theories. Rev. Mod. Phys. 2019, 91, 025001. https://doi.org/10.1103/RevModPhys.91.0 25001

    work page doi:10.1103/revmodphys.91.0 2019

  3. [3]

    Deterministic quantum teleportation of photonic quantum bits by a hybrid technique

    Takeda, S.; Mizuta, T.; Fuwa, M.; van Loock, P .; Furusawa, A. Deterministic quantum teleportation of photonic quantum bits by a hybrid technique. Nature 2013, 500, 315–318. https://doi.org/10.1038/nature12366

    work page doi:10.1038/nature12366 2013

  4. [4]

    Quantum sensing

    Degen, C.L.; Reinhard, F.; Cappellaro, P . Quantum sensing. Rev. Mod. Phys. 2017, 89, 035002. https://doi.org/10.1103/ RevModPhys.89.035002

    2017

  5. [5]

    Quantum cryptography: Public key distribution and coin tossing

    Bennett, C.H.; Brassard, G. Quantum cryptography: Public key distribution and coin tossing. Theor. Comput. Sci. 2014, 560, 7–11. https://doi.org/10.1016/j.tcs.2014.05.025

    doi:10.1016/j.tcs.2014.05.025 2014

  6. [6]

    Quantum Metrology

    Giovannetti, V .; Lloyd, S.; Maccone, L. Quantum Metrology. Phys. Rev. Lett. 2006, 96, 010401. https://doi.org/10.1103/ PhysRevLett.96.010401

    2006

  7. [7]

    Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? Phys

    Einstein, A.; Podolsky, B.; Rosen, N. Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? Phys. Rev. 1935, 47, 777. https://doi.org/10.1103/PhysRev.47.777

    doi:10.1103/physrev.47.777 1935

  8. [8]

    New High-Intensity Source of Polarization-Entangled Photon Pairs

    Kwiat, P .G.; Mattle, K.; Weinfurter, H.; Zeilinger, A.; Sergienko, A.V .; Shih, Y. New High-Intensity Source of Polarization-Entangled Photon Pairs. Phys. Rev. Lett. 1995, 75, 4337. https://doi.org/10.1103/PhysRevLett.75.4337

    doi:10.1103/physrevlett.75.4337 1995

Show all 93 references
  1. [9]

    Modular entanglement of atomic qubits using photons and phonons

    Hucul, D.; Inlek, I.V .; Vittorini, G.; Crocker, C.; Debnath, S.; Clark, S.M.; Monroe, C. Modular entanglement of atomic qubits using photons and phonons. Nat. Phys. 2015, 11, 37. https://doi.org/10.1038/nphys3150

    2015 doi

  2. [10]

    Unconditional Quantum Teleportation

    Furusawa, A.; Sørensen, J.L.; Braunstein, S.L.; Fuchs, C.A.; Kimble, H.J.; Polzik, E.S. Unconditional Quantum Teleportation. Science 1998, 282, 706–709. https://doi.org/10.1126/science.282.5389.706

    1998 doi

  3. [11]

    Quantum communication through spin chain dynamics: An introductory overview

    Bose, S. Quantum communication through spin chain dynamics: An introductory overview. Contemp. Phys. 2007, 48, 13. https://doi.org/10.1080/00107510701342313

    2007 doi

  4. [12]

    Electron wavepacket propagation in a chain of coupled quantum dots.J

    Nikolopoulos, G.M.; Petrosyan, D.; Lambropoulos, P . Electron wavepacket propagation in a chain of coupled quantum dots.J. Phys. Condens. Matter 2004, 16, 4991. https://doi.org/10.1088/0953-8984/16/28/019

    2004 doi

  5. [13]

    Perfect, efficient, state transfer and its application as a constructive tool

    Kay, A. Perfect, efficient, state transfer and its application as a constructive tool. Int. J. Quantum Inf. 2010, 8, 641. https: //doi.org/10.1142/S0219749910006514

    2010 doi

  6. [14]

    Quantum Information and Quantum Computation: Theory and Experiments; Nova Science Publishers: Hauppauge, NY, USA, 2007

    D’Amico, I. Quantum Information and Quantum Computation: Theory and Experiments; Nova Science Publishers: Hauppauge, NY, USA, 2007. https://doi.org/10.1002/pssc.200777631

    2007 doi

  7. [15]

    Magnetic qubits as hardware for quantum computers

    Tejada, J.; Chudnovsky, E.M.; del Barco, E.; Hernandez, J.M.; Spiller, T.P . Magnetic qubits as hardware for quantum computers. Nanotechnology 2001, 12, 181. https://doi.org/10.1088/0957-4484/12/2/323

    2001 doi

  8. [16]

    Quantum-cellular-automata quantum computing with endohedral fullerenes

    Twamley, J. Quantum-cellular-automata quantum computing with endohedral fullerenes. Phys. Rev. A 2003, 67, 052318. https://doi.org/10.1103/PhysRevA.67.052318

    2003 doi

  9. [17]

    Quantum Communication through an Unmodulated Spin Chain

    Bose, S. Quantum Communication through an Unmodulated Spin Chain. Phys. Rev. Lett. 2003, 91, 207901. https://doi.org/10.1 103/PhysRevLett.91.207901

    2003

  10. [18]

    Perfect State Transfer in Quantum Spin Networks

    Christandl, M.; Datta, N.; Ekert, A.; Landahl, A.J. Perfect State Transfer in Quantum Spin Networks. Phys. Rev. Lett. 2004, 92, 187902. https://doi.org/10.1103/PhysRevLett.92.187902. Entropy 2025, 27, 764 18 of 20

    2004 doi

  11. [19]

    Entanglement in a simple quantum phase transition

    Osborne, T.J.; Nielsen, M.A. Entanglement in a simple quantum phase transition. Phys. Rev. A 2002, 66, 032110. https: //doi.org/10.1103/PhysRevA.66.032110

    2002 doi

  12. [20]

    Entanglement in many-body systems

    Amico, L.; Fazio, R.; Osterloh, A.; Vedral, V . Entanglement in many-body systems. Rev. Mod. Phys. 2008, 80, 517. https: //doi.org/10.1103/RevModPhys.80.517

    2008 doi

  13. [21]

    Unitary Design of Quantum Spin Networks for Robust Routing, Entanglement Generation, and Phase Sensing

    Alsulami, A.H.; D’Amico, I.; Estarellas, M.P .; Spiller, T.P . Unitary Design of Quantum Spin Networks for Robust Routing, Entanglement Generation, and Phase Sensing. Adv. Quantum Technol. 2022, 5, 2200013. https://doi.org/10.1002/qute.202200013

    2022 doi

  14. [22]

    Perfect state transfer, effective gates, and entanglement generation in engineered bosonic and fermionic networks

    Yung, M.-H.; Bose, S. Perfect state transfer, effective gates, and entanglement generation in engineered bosonic and fermionic networks. Phys. Rev. A 2005, 71, 032310. https://doi.org/10.1103/PhysRevA.71.032310

    2005 doi

  15. [23]

    Robust quantum entanglement generation and generation-plus-storage protocols with spin chains

    Estarellas, M.P .; D’Amico, I.; Spiller, T.P . Robust quantum entanglement generation and generation-plus-storage protocols with spin chains. Phys. Rev. A 2017, 95, 042335. https://doi.org/10.1103/PhysRevA.95.042335

    2017 doi

  16. [24]

    Long-Distance Entanglement in Spin Systems

    Venuti, L.C.; Boschi, C.D.E.; Roncaglia, M. Long-Distance Entanglement in Spin Systems. Phys. Rev. Lett. 2006, 96, 247206. https://doi.org/10.1103/PhysRevLett.96.247206

    2006 doi

  17. [25]

    Long-distance entanglement and quantum teleportation inXX spin chains

    Venuti, L.C.; Giampaolo, S.M.; Illuminati, F.; Zanardi, P . Long-distance entanglement and quantum teleportation inXX spin chains. Phys. Rev. A 2007, 76, 052328. https://doi.org/10.1103/PhysRevA.76.052328

    2007 doi

  18. [26]

    Long-distance entanglement and quantum teleportation in coupled-cavity arrays

    Giampaolo, S.M.; Illuminati, F. Long-distance entanglement and quantum teleportation in coupled-cavity arrays. Phys. Rev. A 2009, 80, 050301. https://doi.org/10.1103/PhysRevA.80.050301

    2009 doi

  19. [27]

    Coherent electron wavepacket propagation and entanglement in array of coupled quantum dots

    Nikolopoulos, G.M.; Petrosyan, D.; Lambropoulos, P . Coherent electron wavepacket propagation and entanglement in array of coupled quantum dots. Europhys. Lett. 2004, 65, 297. https://doi.org/10.1209/epl/i2003-10100-9

    2004 doi

  20. [28]

    Quantum State Transfer and Network Engineering; Springer: Berlin/Heidelberg, Germany, 2014

    Nikolopoulos, G.M.; Jex, I. Quantum State Transfer and Network Engineering; Springer: Berlin/Heidelberg, Germany, 2014. https://doi.org/10.1007/978-3-642-39937-4

    2014 doi

  21. [29]

    Creating two-qudit maximally entangled quantum link through bulk

    Agarwal, K.D.; Haldar, S.K.; De, A.S. Creating two-qudit maximally entangled quantum link through bulk. arXiv 2024, arXiv:2408.07649

    2024 arXiv

  22. [30]

    Quantum Fisher information and multipartite entanglement in spin-1 chains

    Dell’Anna, F.; Pradhan, S.; Boschi, C.D.E.; Ercolessi, E. Quantum Fisher information and multipartite entanglement in spin-1 chains. Phys. Rev. B 2023, 108, 144414. https://doi.org/10.1103/PhysRevB.108.144414

    2023 doi

  23. [31]

    Entanglement entropy of the random s = 1 Heisenberg chain

    Refael, G.; Moore, J.E. Entanglement entropy of the random s = 1 Heisenberg chain. Phys. Rev. B 2007, 76, 024419. https: //doi.org/10.1103/PhysRevB.76.024419

    2007 doi

  24. [32]

    Rapid and Robust generation of Einstein–Podolsky–Rosen pairs with Spin Chains

    Wilkinson, K.N.; Estarellas, M.P .; Spiller, T.P .; D’amico, I. Rapid and Robust generation of Einstein–Podolsky–Rosen pairs with Spin Chains. Quantum Inf. Comput. 2018, 18, 247. https://doi.org/10.26421/QIC18.3-4

    2018 doi

  25. [33]

    Topologically protected localised states in spin chains

    Estarellas, M.P .; D’Amico, I.; Spiller, T.P . Topologically protected localised states in spin chains. Sci. Rep. 2017, 7, 42904. https://doi.org/10.1038/srep42904

    2017 doi

  26. [34]

    The Peierls distorted chain as a quantum data bus for quantum state transfer.Europhys

    Huo, M.X.; Li, Y.; Song, Z.; Sun, C.P . The Peierls distorted chain as a quantum data bus for quantum state transfer.Europhys. Lett. 2008, 84, 30004. https://doi.org/10.1209/0295-5075/84/30004

    2008 doi

  27. [35]

    Nonlocal dissipative tunneling for high-fidelity quantum-state transfer between distant parties

    Neto, G.; de Ponte, M.; Moussa, M.H.Y. Nonlocal dissipative tunneling for high-fidelity quantum-state transfer between distant parties. Phys. Rev. A 2012, 85, 052303. https://doi.org/10.1103/PhysRevA.85.052303

    2012 doi

  28. [36]

    Robust Quantum State Transfer in Random Unpolarized Spin Chains

    Yao, N.Y.; Jiang, L.; Gorshkov, A.V .; Gong, Z.-X.; Zhai, A.; Duan, L.-M.; Lukin, M.D. Robust Quantum State Transfer in Random Unpolarized Spin Chains. Phys. Rev. Lett. 2011, 106, 040505. https://doi.org/10.1103/PhysRevLett.106.040505

    2011 doi

  29. [37]

    Routing quantum information in spin chains.Phys

    Paganelli, S.; Lorenzo, S.; Apollaro, T.J.; Plastina, F.; Giorgi, G.L. Routing quantum information in spin chains.Phys. Rev. A 2013, 87, 062309. https://doi.org/10.1103/PhysRevA.87.062309

    2013 doi

  30. [38]

    Entanglement generation between distant parties via disordered spin chains

    Almeida, G.M.A.; de Moura, F.A.B.F.; Lyra, M.L. Entanglement generation between distant parties via disordered spin chains. Quantum Inf. Process. 2019, 18, 41. https://doi.org/10.1007/s11128-018-2157-6

    2019 doi

  31. [39]

    Quantum non-Markovianity: characterization, quantification and detection

    Rivas, Á.; Huelga, S.F.; Plenio, M.B. Quantum non-Markovianity: characterization, quantification and detection. Rep. Prog. Phys. 2014, 77, 094001. https://doi.org/10.1088/0034-4885/77/9/094001

    2014 doi

  32. [40]

    Quantum non-Markovianity: Overview and recent developments.Front

    Shrikant, U.; Mandayam, P . Quantum non-Markovianity: Overview and recent developments.Front. Quantum Sci. Technol. 2023, 2, 1134583. https://doi.org/10.3389/frqst.2023.1134583

    2023

  33. [41]

    Stochastic wave-function approach to non-Markovian systems

    Imamog, A. Stochastic wave-function approach to non-Markovian systems. Phys. Rev. A 1994, 50, 3650. https://doi.org/10.1103/ PhysRevA.50.3650

    1994

  34. [42]

    Nonperturbative decay of an atomic system in a cavity.Phys

    Garraway, B.M. Nonperturbative decay of an atomic system in a cavity.Phys. Rev. A 1997, 55, 2290. https://doi.org/10.1103/ PhysRevA.55.2290

    1997

  35. [43]

    Quantum simulations with trapped ions

    Blatt, R.; Roos, C.F. Quantum simulations with trapped ions. Nat. Phys. 2012, 8, 277–284. https://doi.org/10.1038/nphys2252

    2012 doi

  36. [44]

    A quantum engineer’s guide to superconducting qubits

    Krantz, P .; Kjaergaard, M.; Yan, F.; Orlando, T.P .; Gustavsson, S.; Oliver, W.D. A quantum engineer’s guide to superconducting qubits . Appl. Phys. Rev. 2019, 6, 021318. https://doi.org/10.1063/1.5089550

    2019 doi

  37. [45]

    The nitrogen-vacancy colour centre in diamond

    Doherty, M.W.; Manson, N.B.; Delaney, P .; Jelezko, F.; Wrachtrup, J.; Hollenberg, L.C.L. The nitrogen-vacancy colour centre in diamond. Phys. Rep. 2013, 528, 1–45. https://doi.org/10.1016/j.physrep.2013.02.001

    2013 doi

  38. [46]

    Spins in few-electron quantum dots.Rev

    Hanson, R.; Kouwenhoven, L.P .; Petta, J.R.; Tarucha, S.; Vandersypen, L.M.K. Spins in few-electron quantum dots.Rev. Mod. Phys. 2007, 79, 1217. https://doi.org/10.1103/RevModPhys.79.1217. Entropy 2025, 27, 764 19 of 20

    2007 doi

  39. [47]

    Robust entanglement in antiferromagnetic Heisenberg chains by single-spin optimal control

    Wang, X.; Bayat, A.; Schirmer, S.G.; Bose, S. Robust entanglement in antiferromagnetic Heisenberg chains by single-spin optimal control. Phys. Rev. A 2010, 81, 032312. https://doi.org/10.1103/PhysRevA.81.032312

    2010 doi

  40. [48]

    Creation and manipulation of entanglement in spin chains far from equilibrium

    Galve, F.; Zueco, D.; Reuther, G.M.; Kohler, S.; Hänggi, P . Creation and manipulation of entanglement in spin chains far from equilibrium. Eur. Phys. J. Spec. Top. 2010, 180, 237–246. https://doi.org/10.1140/epjst/e2010-01220-5

    2010 doi

  41. [49]

    Ballistic entanglement cloud after a boundary quench.Phys

    Alkurtass, B.; Bayat, A.; Sodano, P .; Bose, S.; Johannesson, H. Ballistic entanglement cloud after a boundary quench.Phys. Rev. Res. 2025, 7, 013268. https://doi.org/10.1103/PhysRevResearch.7.013268

    2025 doi

  42. [50]

    (Eds.) Entanglement in Spin Chains: From Theory to Quantum Technology Applications; Quantum Science and Technology; Springer: Cham, Switzerland, 2022

    Bayat, A.; Bose, S.; Johannesson, H. (Eds.) Entanglement in Spin Chains: From Theory to Quantum Technology Applications; Quantum Science and Technology; Springer: Cham, Switzerland, 2022. https://doi.org/10.1007/978-3-031-03998-0

    2022 doi

  43. [51]

    On the generators of quantum dynamical semigroups

    Lindblad, G. On the generators of quantum dynamical semigroups. Commun. Math. Phys. 1976, 48, 119–130. https://doi.org/10.1 007/BF01608499

    1976

  44. [52]

    Completely positive dynamical semigroups of N-level systems.J

    Gorini, V .; Kossakowski, A.; Sudarshan, E.C.G. Completely positive dynamical semigroups of N-level systems.J. Math. Phys. 1976, 17, 821–825. https://doi.org/10.1063/1.522979

    1976 doi

  45. [53]

    A short introduction to the Lindblad master equation.AIP Adv

    Manzano, D. A short introduction to the Lindblad master equation.AIP Adv. 2020, 10, 025106. https://doi.org/10.1063/1.5115323

    2020 doi

  46. [54]

    Rabi Oscillations in a Large Josephson-Junction Qubit

    Martinis, J.M.; Nam, S.; Aumentado, J.; Urbina, C. Rabi Oscillations in a Large Josephson-Junction Qubit. Phys. Rev. Lett. 2002, 89, 117901. https://doi.org/10.1103/PhysRevLett.89.117901

    2002 doi

  47. [55]

    Suppressing charge noise decoherence in superconducting charge qubits

    Schreier, J.A.; Houck, A.A.; Koch, J.; Schuster, D.I.; Johnson, B.R.; Chow, J.M.; Gambetta, J.M.; Majer, J.; Frunzio, L.; Devoret, M.H.; Girvin, S.M.; Schoelkopf, R.J. Suppressing charge noise decoherence in superconducting charge qubits. Phys. Rev. B 2008, 77, 180502. https:/...

    2008 doi

  48. [56]

    Superconducting quantum bits

    Clarke, J.; Wilhelm, F.K. Superconducting quantum bits. Nature 2008, 453, 1031–1042. https://doi.org/10.1038/nature07128

    2008 doi

  49. [57]

    A quantum information processor with trapped ions

    Schindler, P .; Barreiro, J.T.; Monz, T.; Nebendahl, V .; Nigg, D.; Chwalla, M.; Hennrich, M.; Roos, C.F.; Blatt, R. A quantum information processor with trapped ions. New J. Phys. 2013, 15, 123012. https://doi.org/10.1088/1367-2630/15/12/123012

    2013 doi

  50. [58]

    Many-body physics with ultracold gases

    Bloch, I.; Dalibard, J.; Zwerger, W. Many-body physics with ultracold gases. Rev. Mod. Phys. 2008, 80, 885. https://doi.org/10.110 3/RevModPhys.80.885

    2008

  51. [59]

    Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond

    Lewenstein, M.; Sanpera, A.; Ahufinger, V .; Damski, B.; Sen, A.; Sen, U. Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond. Adv. Phys. 2007, 56, 243–379. https://doi.org/10.1080/00018730701223200

    2007 doi

  52. [60]

    Separability Criterion for Density Matrices.Phys

    Peres, A. Separability Criterion for Density Matrices.Phys. Rev. Lett. 1996, 77, 1413. https://doi.org/10.1103/PhysRevLett.77.1413

    1996 doi

  53. [61]

    Separability of mixed states: Necessary and sufficient conditions.Phys

    Horodecki, M.; Horodecki, P .; Horodecki, R. Separability of mixed states: Necessary and sufficient conditions.Phys. Lett. A 1996, 223, 1–8. https://doi.org/10.1016/S0375-9601(96)00706-2

    1996 doi

  54. [62]

    Computable measure of entanglement.Phys

    Vidal, G.; Werner, R.F. Computable measure of entanglement.Phys. Rev. A 2002, 65, 032314. https://doi.org/10.1103/PhysRevA. 65.032314

    2002 doi

  55. [63]

    Quantum Computation and Quantum Information; Cambridge University Press: Cambridge, UK, 2010

    Nielsen, M.A.; Chuang, I.L. Quantum Computation and Quantum Information; Cambridge University Press: Cambridge, UK, 2010. https://doi.org/10.1017/CBO9780511976667

    2010 doi

  56. [64]

    Lower bounds on concurrence and separability conditions

    Vicenti, J.I. Lower bounds on concurrence and separability conditions. Phys. Rev. A 2007, 75, 052320. https://doi.org/10.1103/ PhysRevA.75.052320

    2007

  57. [65]

    Quantum computation and quantum-state engineering driven by dissipation

    Verstraete, F.; Wolf, M.M.; Cirac, J.I. Quantum computation and quantum-state engineering driven by dissipation. Nat. Phys. 2009, 5, 633–636. https://doi.org/10.1038/nphys1342

    2009 doi

  58. [66]

    Dissipative production of a maximally entangled steady state of two quantum bits

    Lin, Y.; Gaebler, J.; Reiter, F.; Tan, T.; Bowler, R.; Sørensen, A.; Leibfried, D.; Wineland, D. Dissipative production of a maximally entangled steady state of two quantum bits. Nature 2013, 504, 415–418. https://doi.org/10.1038/nature12801

    2013 doi

  59. [67]

    Entanglement generation between distant spins via quasilocal reservoir engineering

    Dias, J.; Wächtler, C.W.; Nemoto, K.; Munro, W.J. Entanglement generation between distant spins via quasilocal reservoir engineering. Phys. Rev. Res. 2023, 5, 043295. https://doi.org/10.1103/PhysRevResearch.5.043295

    2023 doi

  60. [68]

    Deterministic quantum state transfer and remote entanglement using microwave photons

    Kurpiers, P .; Magnard, P .; Walter, T.; Royer, B.; Pechal, M.; Heinsoo, J.; Salathé, Y.; Akin, A.; Storz, S.; Besse, J.-C.; et al. Deterministic quantum state transfer and remote entanglement using microwave photons. Nature 2018, 558, 264–267. https: //doi.org/10.1038/s41586-...

    2018 doi

  61. [69]

    Localization and topology protected quantum coherence at the edge of hot matter

    Bahri, Y.; Vosk, R.; Altman, E.; Vishwanath, A. Localization and topology protected quantum coherence at the edge of hot matter. Nat. Commun. 2015, 6, 7341. https://doi.org/10.1038/ncomms8341

    2015 doi

  62. [70]

    Master equations for effective Hamiltonians

    Klimov, A.B.; Romero, J.L.; Delgado, J.; Soto, L.L.S.N. Master equations for effective Hamiltonians. J. Opt. B Quantum Semiclass. Opt. 2002, 5, 34. https://doi.org/10.1088/1464-4266/5/1/304

    2002 doi

  63. [71]

    Effective formalism for open-quantum-system dynamics: Time-coarse-graining approach

    Lee, C.-W.; Noh, C.; Kim, J. Effective formalism for open-quantum-system dynamics: Time-coarse-graining approach. Phys. Rev. A 2018, 97, 012102. https://doi.org/10.1103/physreva.97.012102

    2018 doi

  64. [72]

    Quantum Computing in the NISQ era and beyond

    Preskill, J. Quantum Computing in the NISQ era and beyond. Quantum 2018, 2, 79. https://doi.org/10.22331/q-2018-08-06-79

    2018 doi

  65. [73]

    Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits

    Müller, C.; Lisenfeld, J.; Shnirman, A.; Poletto, S. Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits. Phys. Rev. B 2015, 92, 035442. https://doi.org/10.1103/PhysRevB.92.035442

    2015 doi

  66. [74]

    Pure quantum dephasing of a solid-state electron spin qubit in a large nuclear spin bath coupled by long-range hyperfine-mediated interactions

    Cywin, Ł.; Witzel, W.M.; Sarma, S.D. Pure quantum dephasing of a solid-state electron spin qubit in a large nuclear spin bath coupled by long-range hyperfine-mediated interactions. Phys. Rev. B 2009, 79, 245314. https://doi.org/10.1103/PhysRevB.79.245 314. Entropy 2025, 27, 76...

    2009 doi

  67. [75]

    Stochastic Liouville, Langevin, Fokker–Planck, and Master Equation Approaches to Quantum Dissipative Systems

    Tanimura, Y. Stochastic Liouville, Langevin, Fokker–Planck, and Master Equation Approaches to Quantum Dissipative Systems. J. Phys. Soc. Jpn. 2006, 75, 082001. https://doi.org/10.1143/JPSJ.75.082001

    2006 doi

  68. [76]

    Classical counterexamples to Bell’s inequalities.Phys

    Breuer, H.-P .; Petruccione, F. Classical counterexamples to Bell’s inequalities.Phys. Rev. A 2002, 65, 042106. https://doi.org/10.1 103/PhysRevA.65.042106

    2002

  69. [77]

    Non-Markovian quantum state diffusion.Phys

    Diósi, L.; Gisin, N.; Strunz, W.T. Non-Markovian quantum state diffusion.Phys. Rev. A 1998, 58, 1699. https://doi.org/10.1103/ PhysRevA.58.1699

    1998

  70. [78]

    Exact mapping between system-reservoir quantum models and semi-infinite discrete chains using orthogonal polynomials

    Chin, A.W.; Rivas, Á.; Huelga, S.F.; Plenio, M.B. Exact mapping between system-reservoir quantum models and semi-infinite discrete chains using orthogonal polynomials. J. Math. Phys. 2010, 51, 092109. https://doi.org/10.1063/1.3490188

    2010 doi

  71. [79]

    Circuit quantum electrodynamics

    Blais, A.; Grimsmo, A.L.; Girvin, S.M.; Wallraff, A. Circuit quantum electrodynamics. Rev. Mod. Phys. 2021, 93, 025005. https://doi.org/10.1103/RevModPhys.93.025005

    2021 doi

  72. [80]

    Single-molecule strong coupling at room temperature in plasmonic nanocavities

    Chikkaraddy, R.; de Nijs, B.; Benz, F.; Barrow, S.J.; Scherman, O.A.; Rosta, E.; Demetriadou, A.; Fox, P .; Hess, O.; Baumberg, J.J. Single-molecule strong coupling at room temperature in plasmonic nanocavities. Nature 2016, 535, 127–130. https://doi.org/10.1 038/nature17974

    2016

  73. [81]

    Method for universal detection of two-photon polarization entanglement

    Leghtas, Z.; Touzard, S.; Pop, I.M.; Kou, A.; Vlastakis, B.; Petrenko, A.; Sliwa, K.M.; Narla, A.; Shankar, S.; Hatridge, M.J.; et al. Method for universal detection of two-photon polarization entanglement. Phys. Rev. A 2015, 91, 032315. https://doi.org/10.1103/ PhysRevA.91.032315

    2015

  74. [82]

    Tensor products of process matrices with indefinite causal structure

    Jia, D.; Sakharwade, N. Tensor products of process matrices with indefinite causal structure. Phys. Rev. A 2018, 97, 032110. https://doi.org/10.1103/PhysRevA.97.032110

    2018 doi

  75. [83]

    Efficient Simulation of Finite-Temperature Open Quantum Systems.Phys

    Tamascelli, D.; Smirne, A.; Huelga, S.F.; Plenio, M.B. Efficient Simulation of Finite-Temperature Open Quantum Systems.Phys. Rev. Lett. 2019, 123, 090402. https://doi.org/10.1103/PhysRevLett.123.090402

    2019 doi

  76. [84]

    Transient Chaotic Dimensionality Expansion by Recurrent Networks.Phys

    Keup, C.; Kühn, T.; Dahmen, D.; Helias, M. Transient Chaotic Dimensionality Expansion by Recurrent Networks.Phys. Rev. X 2021, 11, 021064. https://doi.org/10.1103/PhysRevX.11.021064

    2021 doi

  77. [85]

    QuTiP 2: A Python framework for the dynamics of open quantum systems

    Johansson, J.; Nation, P .; Nori, F. QuTiP 2: A Python framework for the dynamics of open quantum systems. Comput. Phys. Commun. 2013, 184, 1234–1240. https://doi.org/10.1016/j.cpc.2012.11.019

    2013 doi

  78. [86]

    Dynamics of non-Markovian open quantum systems

    De Vega, I.; Alonso, D. Dynamics of non-Markovian open quantum systems. Rev. Mod. Phys. 2017, 89, 015001. https: //doi.org/10.1103/RevModPhys.89.015001

    2017 doi

  79. [87]

    Ultrastrong coupling regimes of light-matter interaction.Rev

    Forn-Díaz, P .; Lamata, L.; Rico, E.; Kono, J.; Solano, E. Ultrastrong coupling regimes of light-matter interaction.Rev. Mod. Phys. 2019, 91, 025005. https://doi.org/10.1103/RevModPhys.91.025005

    2019 doi

  80. [88]

    Colored channels for high-fidelity information transfer and processing between remote multi-branch quantum circuits

    de Moraes Neto, G.; de Ponte, M.; Moussa, M.H.Y. Colored channels for high-fidelity information transfer and processing between remote multi-branch quantum circuits. Europhys. Lett. 2013, 103, 43001. https://doi.org/10.1209/0295-5075/103/43001

    2013 doi

  81. [89]

    Spin-Chain-Star Systems: Entangling Multiple Chains of Spin Qubits

    Grimaudo, R.; de Castro, A.S.M.; Messina, A.; Valenti, D. Spin-Chain-Star Systems: Entangling Multiple Chains of Spin Qubits. Fortschr. Phys. 2022, 70, 2200042. https://doi.org/10.1002/prop.202200042

    2022 doi

  82. [90]

    Steady many-body entanglements in dissipative systems.Phys

    de Moraes Neto, G.; Teizen, V .; Montenegro, V .; Vernek, E. Steady many-body entanglements in dissipative systems.Phys. Rev. A 2017, 96, 062313. https://doi.org/10.1103/PhysRevA.96.062313

    2017 doi

  83. [91]

    Programmable quantum simulations of spin systems with trapped ions

    Monroe, C.; Campbell, W.C.; Duan, L.-M.; Gong, Z.-X.; Gorshkov, A.V .; Hess, P .W.; Islam, R.; Kim, K.; Linke, N.M.; Pagano, G.; et al. Programmable quantum simulations of spin systems with trapped ions. Rev. Mod. Phys. 2021, 93, 025001. https: //doi.org/10.1103/RevModPhys.93.025001

    2021 doi

  84. [92]

    Experimental Realization of the Rabi-Hubbard Model with Trapped Ions

    Mei, Q.-X.; Wang, B.-Z.; Yang, T.; Chen, Y.; Wu, J.; Wang, P .; Zhang, X.; Tan, T.; Qiao, Y.; Cui, J.-M.; Pan, J.-W. Experimental Realization of the Rabi-Hubbard Model with Trapped Ions. Phys. Rev. Lett. 2022, 128, 160504. https://doi.org/10.1103/ PhysRevLett.128.160504

    2022

  85. [93]

    Qubit-oscillator dynamics in the dispersive regime: Analytical theory beyond the rotating-wave approximation

    Zueco, D.; Reuther, G.M.; Kohler, S.; Hänggi, P . Qubit-oscillator dynamics in the dispersive regime: Analytical theory beyond the rotating-wave approximation. Phys. Rev. A 2009, 80, 033846. https://doi.org/10.1103/PhysRevA.80.033846. Disclaimer/Publisher’s Note: The statement...

    2009 doi

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