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Measurement-Induced Quantum Zeno Control of Tunneling in a Two-Level Model: A Monte-Carlo Unraveling Study with Effective Measurement-Rate Scaling

Zuhair Ahmed

Published Jan 1, 2026• 0 citations
Publisher

Abstract

Abstract We present a numerical study of measurement-induced suppression of coherent tunneling in a two-level quantum system subject to re peated projective monitoring. The dynamics are simulated using a stochastic quantum-trajectory (Monte-Carlo) unraveling which repro duces the dephasing dynamics of a continuously monitored system. We introduce an effective measurement rate γ ≈ pmeas/dt and demon strate a monotonic reduction of the escaped population as a function of γ/∆, where ∆ is the coherent tunneling amplitude. For a fixed evolution time T = π/2, we observe a clear transition to the quantum Zeno regime for γ ≫ ∆. A log–log analysis of the large-γ data re veals an asymptotic scaling close to Pesc ∝ γ−1, in agreement with the strong-measurement limit of the corresponding Lindblad master equation. Our results provide a compact and programmable numerical platform for investigating measurement-controlled tunneling dynamics and Zeno-based control using gate-level quantum simulation frame works.

DOI
10.21203/rs.3.rs-8799450/v1

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Abstract We present a numerical study of measurement-induced suppression of coherent tunneling in a two-level quantum system subject to re peated projective monitoring. The dynamics are simulated using a stochastic quantum-trajectory (Monte-Carlo) unraveling which repro duces the dephasing dynamics of a continuously monitored system. We introduce an effective measurement rate γ ≈ pmeas/dt and demon strate a monotonic reduction of the escaped population as a function of γ/∆, where ∆ is the coherent tunneling amplitude. For a fixed evolution time T = π/2, we observe a clear transition to the quantum Zeno regime for γ ≫ ∆. A log–log analysis of the large-γ data re veals an asymptotic scaling close to Pesc ∝ γ−1, in agreement with the strong-measurement limit of the corresponding Lindblad master equation. Our results provide a compact and programmable numerical platform for investigating measurement-controlled tunneling dynamics and Zeno-based control using gate-level quantum simulation frame works.
We present a numerical study of measurement-induced suppressionof coherent tunneling in a two-level quantum system subject to repeated projective monitoring. The dynamics are simulated using astochastic quantum-trajectory (Monte-Carlo) unraveling which reproduces the dephasing dynamics of a continuously monitored system.We introduce an effective measurement rate γ ≈ pmeas/dt and demonstrate a monotonic reduction of the escaped population as a functionof γ/∆, where ∆ is the coherent tunneling amplitude. For a fixedevolution time T = π/2, we observe a clear transition to the quantumZeno regime for γ ≫ ∆. A log–log analysis of the large-γ data reveals an asymptotic scaling close to Pesc ∝ γ−1, in agreement withthe strong-measurement limit of the corresponding Lindblad masterequation. Our results provide a compact and programmable numericalplatform for investigating measurement-controlled tunneling dynamicsand Zeno-based control using gate-level quantum simulation frameworks.
We present a theoretical and numerical study of measurement-induced phase transitions and quantum Zeno dynamics in continuously monitored open many-body systems. Moving beyond closed unitary systems, we investigate the competition between chaotic unitary evolution and continuous weak measurements by employing the stochastic Schrödinger equation (quantum jump Monte Carlo) formalism and non-hermitian effective Hamiltonians. Our analysis examines the transition from area-law to volume-law entanglement scaling, mutual information properties, and the critical scaling hypothesis near the measurement-rate threshold. Furthermore, we derive original analytical estimates for the quantum correlation damping decrement in the regime of strong Zeno suppression and validate the theoretical findings using stochastic trajectory numerical simulation protocols with finite-size scaling.
We explore the Quantum Zeno Effect (QZE) as a dynamical mechanism for suppressing quantum information transport in open systems. Moving beyond the phenomenological decay of survival probabilities in zero-dimensional systems, we utilize a continuous measurement effective model governed by the Stochastic Schrödinger Equation (SSE). Our numerical investigations suggest that measurement-induced freezing can be mapped to the behavior of a Liouvillian Exceptional Point (EP). We demonstrate how this non-unitary backaction manifests in our simulations: from suppressing single-particle spatial transmission (showing a trend consistent with T ∝ γ^(-α)), to the qualitative reduction of information scrambling as indicated by the Tripartite Mutual Information (I₃ → 0). Finally, scaling this effective model to finite XXZ spin chains (N ≤ 10), our data indicates a transition-like behavior from volume-law to area-law entanglement scaling. While bounded by finite-size limitations, our results provide numerical evidence supporting the interpretation of Zeno dynamics as a suppressor of information geometry.
We investigate measurement-induced localization in a continuously monitored one-dimensional Aubry--André--Harper model, focusing on the quantum Zeno regime in which the measurements dominate coherent dynamics. The presence of a quasiperiodic potential renders the problem analytically tractable and enables a controlled study of the interplay between monitoring and disorder. We develop an analytical description based on an instantaneous Schrödinger equation with a measurement-induced effective potential constructed self-consistently from individual quantum trajectories, without relying on postselection. In the quantum Zeno regime, an emergent dominant energy scale reduces the problem to a transfer-matrix formulation of an effective non-Hermitian Hamiltonian, which allows direct computation of the Lyapunov exponent. Complementarily, we extract the localization length numerically from long-time steady-state quantum state diffusion trajectories by reconstructing the intrinsic localized single-particle wave functions and analyzing their spatial decay. These numerical results show quantitative agreement with the effective theory predictions, with controlled corrections of order J2/[λ2+(γ/2)2]J^2/[λ^2+(γ/2)^2]J2/[λ2+(γ/2)2] (where JJJ is the hopping amplitude, γγγ the measurement strength, and λλλ the quasiperiodic potential). Our results underscore the connection between the effective non-Hermitian description and the stochastic monitored dynamics, showing the interplay between Zeno-like localization, coherent hopping, and quasiperiodic-disorder-induced localization, while also laying the groundwork for understanding and exploiting measurement-induced localization as a tool for quantum control and state preparation.
The quantum Zeno effect is a distinctive phenomenon in quantum mechanics, describing the nontrivial effect of frequent projective measurements on hindering the evolution of a quantum system. However, when subjected to environmental noise, the quantum system may dissipate, and the quantum Zeno effect no longer works. This research starts from the physical mechanism for the decay of the quantum Zeno effect in the presence of noise and investigates the effect of coherent quantum controls on mitigating the decrease of the survival probability that the system stays in the initial state induced by the noise. We derive the decay rate of the survival probability with and without coherent quantum controls in general, and show that when the frequency of the projective measurements is large but finite, proper coherent controls by sufficiently strong Hamiltonians can be designed to decrease the decay rate of the survival probability. A two-level quantum system suffering from typical unitary and nonunitary noise is then considered to demonstrate the effect of the proposed coherent quantum control scheme in protecting the quantum Zeno effect against the noise. The decay rate of the survival probability is obtained in the presence of noise, and the control Hamiltonian is further optimized analytically to minimize the decay rate by a variational approach. The evolution paths of the quantum system with the optimal coherent controls are illustrated numerically for different scenarios to explicitly show how the coherent control scheme works in lowering the decay of survival probability.
The quantum Zeno and anti-Zeno effects describe how frequent measurements can either suppress or accelerate quantum dynamics. While extensively studied in various platforms, their manifestation in dark-state dynamics remains largely unexplored. Here we investigate the stability of dark states in a cavity quantum electrodynamics (QED) system consisting of two atoms coupled to a single-mode cavity, subject to thermal dephasing that models continuous quantum non-demolition monitoring. Using the Tavis--Cummings model within a Lindblad master equation framework, we perform numerical simulations to investigate how measurement-induced dephasing affects dark-state retention and stabilization time. Through systematic numerical scans, we identify distinct parameter regimes corresponding to Zeno and anti-Zeno behavior: at low dephasing intensities, increasing the measurement strength accelerates the loss of dark-state coherence (anti-Zeno regime), while at higher intensities, it slows down the dynamics and partially recovers dark-state weight (Zeno regime). The transition between these regimes is controlled by the dephasing rates, the cavity photon exchange, and the asymmetry in atom--field couplings. We show that even under strong dephasing, a finite dark-state component persists, demonstrating remarkable robustness. Our results provide insights into the interplay between measurement back-action and decoherence in open quantum systems, with implications for quantum control and information storage.