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Theoretical and Natural Science

Dynamics of Quantum Entanglement in Transverse-Field Ising-Interacting Two-Qubit Systems Subject to Local Amplitude Decoherence

Kaiyang Liu

Published May 18, 2026• 0 citations
Publisher

Abstract

Quantum entanglement is a cornerstone of quantum technologies, but its susceptibility to environmental noise hinders practical implementations. This study investigates the entanglement dynamics in a two-qubit system governed by a transverse-field Ising Hamiltonian and exposed to local amplitude decoherence via the Lindblad master equation. Beginning with a maximally entangled Bell state, we numerically integrate the density matrix evolution using QuTiP. Entanglement, measured by concurrence, displays oscillatory decay influenced by the coupling J, transverse field B, and decoherence rate γ. Analytical benchmarks, including the unitary limit C(t) ≈ |cos(2Bt)| and non-interacting limit C(t) =ⅇ−2γt, corroborate the simulations. Scans across J/γ reveal that for |J|/γ > 1, entanglement lifetime (time until C < 0.5) can extend by factors of 2–10 relative to weak coupling cases, attributed to interaction-induced level splitting that mitigates damping. Bloch vectors exhibit spiraling contraction in the x-z plane toward the excited state pole, while von Neumann entropy rises in tandem with disentanglement, underscoring decoherence-driven mixing. Local observables such as 〈σ_z〉 oscillate amid relaxation to near-zero equilibrium. At finite temperature (T = 10 mK, n_th = 0.01), lifetime shortens by ~10–20% due to thermal excitations. Anchored in parameters from IBM Eagle and Google Sycamore processors, these results elucidate interaction's protective role against decoherence, offering design guidelines for resilient superconducting qubits in quantum computing and sensing. This work resolves prior inconsistencies in interaction-damping interplay and proposes testable conjectures for entanglement plateaus at specific J/γ ratios.

DOI
10.54254/2753-8818/2026.dl33671

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Quantum entanglement is a cornerstone of quantum technologies, but its susceptibility to environmental noise hinders practical implementations. This study investigates the entanglement dynamics in a two-qubit system governed by a transverse-field Ising Hamiltonian and exposed to local amplitude decoherence via the Lindblad master equation. Beginning with a maximally entangled Bell state, we numerically integrate the density matrix evolution using QuTiP. Entanglement, measured by concurrence, displays oscillatory decay influenced by the coupling J, transverse field B, and decoherence rate γ. Analytical benchmarks, including the unitary limit C(t) ≈ |cos(2Bt)| and non-interacting limit C(t) =ⅇ−2γt, corroborate the simulations. Scans across J/γ reveal that for |J|/γ > 1, entanglement lifetime (time until C < 0.5) can extend by factors of 2–10 relative to weak coupling cases, attributed to interaction-induced level splitting that mitigates damping. Bloch vectors exhibit spiraling contraction in the x-z plane toward the excited state pole, while von Neumann entropy rises in tandem with disentanglement, underscoring decoherence-driven mixing. Local observables such as 〈σ_z〉 oscillate amid relaxation to near-zero equilibrium. At finite temperature (T = 10 mK, n_th = 0.01), lifetime shortens by ~10–20% due to thermal excitations. Anchored in parameters from IBM Eagle and Google Sycamore processors, these results elucidate interaction's protective role against decoherence, offering design guidelines for resilient superconducting qubits in quantum computing and sensing. This work resolves prior inconsistencies in interaction-damping interplay and proposes testable conjectures for entanglement plateaus at specific J/γ ratios.
Abstract Entanglement is an essential resource for quantum information processing; however, it is highly susceptible to decoherence induced by environmental interactions. In this work, we investigate the entanglement dynamics of a two-qubit system subjected to Markovian noise and explore the effectiveness of external control fields in preserving quantum correlations. Using the Lindblad master equation, we model the evolution of the system under two decoherence channels, namely, amplitude damping (spontaneous emission) and phase damping (dephasing). We introduce periodic driving and optimal control protocols to mitigate entanglement loss and analyze their impact using concurrence as a quantifier of two-qubit entanglement. Our numerical results reveal certain conditions under which sudden death of entanglement can be delayed or even prevented. Additionally, in the case of the initial state being a mixed state, we identify time regimes where entanglement revival occurs, providing insights into quantum error correction strategies. The results contribute to the broader understanding of quantum coherence preservation and have implications for quantum computing, secure quantum communication, and quantum memory design.
We study the dynamics of disentanglement of two qubits initially prepared in a Bell state and coupled at different sites to an Ising spin chain in a transverse field (ITF) playing the role of a dynamic spin environment. The initial state of the whole system is prepared in a tensor product state ${\ensuremath{\rho}}_{\mathrm{Bell}}\ensuremath{\bigotimes}{\ensuremath{\rho}}_{\mathrm{chain}}$, where the state of the chain is taken to be given by the ground state $|G({\ensuremath{\lambda}}_{i})\ensuremath{\rangle}$ of the ITF Hamiltonian ${H}_{E}({\ensuremath{\lambda}}_{i})$ with an initial field ${\ensuremath{\lambda}}_{i}$. At time t=0+t={0}^{+}t=0+, the strength of the transverse field is suddenly quenched to a new value, ${\ensuremath{\lambda}}_{f}$, and the whole system (chain +++ qubits) undergoes a unitary dynamics generated by the total Hamiltonian ${H}_{\mathrm{Tot}}={H}_{E}({\ensuremath{\lambda}}_{f})+{H}_{I}$, where HI{H}_{I}HI​ describes a local interaction between the qubits and the spin chain. The resulting dynamics leads to a disentanglement of the qubits, which is described through Wootters' concurrence, due to their interaction with the nonequilibrium environment. The concurrence is related to the Loschmidt echo, which in turn is expressed in terms of the time-dependent covariance matrix associated with the ITF. This permits a precise numerical and analytical analysis of the disentanglement dynamics of the qubits as a function of their distance, bath properties, and quench amplitude. In particular, we emphasize the special role played by a critical initial environment.
We systematically characterize quantum entanglement in all sixteen combinations of two-qubit Bell states across three operational regimes: pure superposition, noiseless mixing, and asymmetric mixing of one noisy and one pure Bell state. For pure superpositions, we calculate the von Neumann entropy and show that entanglement depends critically on the relative phase phi between superposed states. For mixed states, we use concurrence C under three physically motivated decoherence channels. The Depolarizing (DP) and Phase Damping (PD) channels are modeled as global, collective operations on the two-qubit Hilbert space, while Amplitude Damping (AD) is treated as independent local decay on each qubit, reflecting the asymmetric, energy-dissipating nature of spontaneous emission. A central and counterintuitive result is that increasing noise can raise concurrence in specific parameter regimes across all three channels. We further map the boundary between mathematical entanglement (C > 0) and operational quantum non-locality using the Horodecki criterion, finding this boundary to be strongly channel-dependent. Under Phase Damping, the Bell-local entanglement regime vanishes entirely for identical and same-bases mixtures, meaning any surviving entanglement guarantees a CHSH violation. Under Depolarizing noise, a large Bell-local region requires mixing probability r > 1/sqrt(2) to recover non-locality at maximum noise. For Amplitude Damping, certain mixtures exhibit a non-monotonic Horodecki parameter M(T): concurrence decreases monotonically with noise, yet the capacity for CHSH violation is lost at intermediate noise levels and restored at high noise, as maximal damping repurifies the noisy branch. These results provide a unified analytical reference for entanglement and non-locality management across Bell-state combinations and decoherence channels relevant to NISQ architectures.
We present a comprehensive analytical and numerical study of time-dependent decoherence in open quantum systems, focusing on a single-qubit model with time-varying Lindblad dissipation rates. Employing a master equation framework, we derive exact solutions for the evolution of off-diagonal density matrix elements and characterize the emergence of robust pointer states. Our findings reveal an initial rapid coherence decay followed by a gradual slowdown, mirroring experimental trends observed in superconducting qubits influenced by quasiparticle dynamics and in photonic cavities subject to fluctuating environments. By incorporating real experimental parameters and validating the model through quantum simulations using QuTiP, we provide a robust quantitative tool for analyzing decoherence in quantum technologies. This extended model addresses limitations in static-rate approximations, offering insights into non-Markovian effects without resolving the measurement problem, and suggests extensions to multi-qubit systems.
We investigate the time evolution of bipartite quantum correlations in the ground-state hyperfine manifold of the hydrogen atom subjected to an external magnetic field and independent Markovian dephasing. Treating the electron–proton spin pair as an effective two-qubit system, we derive the exact solution of the Lindblad master equation for an X-shaped initial state and quantify the dynamics using three complementary measures: entanglement of formation (through concurrence), quantum steering (through the CJWR inequality) and Bell nonlocality (through normalized CHSH violation). The dynamics are obtained within a unified open-system framework that combines hyperfine interaction, Zeeman splitting, and Markovian dissipation in a single analytically solvable Lindblad model, allowing a complete operator-level characterization of the correlation decay. This exact treatment provides a transparent link between the underlying spectral structure of the Hamiltonian and the observed hierarchy in the robustness of quantum correlations. Our results reveal that all three quantities exhibit damped oscillations whose frequency and decay rate are strongly tuned by the proton magnetic parameter through the Zeeman splitting. While entanglement decays relatively quickly, steering persists noticeably longer and Bell nonlocality proves to be the most fragile, confirming the expected hierarchy of quantum correlations under local dephasing. The external magnetic field emerges as a practical control knob that can extend the lifetime of these resources even in the presence of noise. These findings provide a clear physical picture of how hyperfine coupling, Zeeman effects, and environmental fluctuations jointly govern quantum coherence in atomic spin systems, with direct implications for spin-based quantum technologies and fundamental tests of nonlocality in realistic laboratory settings.
This study advances the theoretical understanding of decoherence mechanisms in open quantum systems by modelling entanglement dynamics under localised environmental interactions relevant to emerging quantum technologies in Tunisia. A unified analytical framework is developed that bridges Markovian and non-Markovian regimes, quantifying the resilience of bipartite entanglement against structured environmental noise. Considering a system of two non-interacting qubits coupled to a common bosonic reservoir, a generalised master equation incorporating a memory kernel is derived from a structured spectral density function with tunable ohmicity. An analytical expression for the time-dependent concurrence is obtained for an initial Bell state, revealing a crossover from monotonic decay to oscillatory behaviour with entanglement revivals as the reservoir cutoff frequency is lowered relative to the qubit splitting. In the sub-ohmic regime, entanglement decay is slower and revivals are more pronounced, demonstrating that the spectral density cutoff frequency acts as a control parameter for entanglement preservation. The framework incorporates a local noise temperature parameter to represent cryostat fluctuations typical of Tunisian laboratory conditions, allowing the model to capture the phenomenology of entanglement evolution under constraints of limited cryogenic infrastructure and higher ambient noise levels. Crucially, the results show that standard Markovian models systematically overestimate the rate of entanglement loss, particularly in sub-ohmic environments, and that non-Markovian memory effects can temporarily restore quantum correlations after periods of apparent death. These findings challenge the assumption that decoherence is irreversible, revealing a form of quantum memory that could be harnessed for error correction or state protection. The framework provides a practical tool for predicting coherence lifetimes in solid-state and photonic systems, offering a comparative benchmark for experimental platforms within Tunisia's nascent quantum optics community and informing the design of robust quantum information protocols in the North African research context.