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arXiv:2410.05394 · Physical Review Research

Measurement-induced phase transitions in monitored infinite-range interacting systems

Anna Delmonte, Zejian Li, Gianluca Passarelli, Eric Yilun Song, Diego Barberena, Ana María Rey, Rosario Fazio

Published Apr 24, 2025• 14 citations
arXivHTMLPDF

Abstract

A key challenge in observing measurement-induced phase transitions is the mitigation of the post-selection barrier, which causes the reproducibility of specific sequences of measurement readouts—the trajectory—to be exponentially small in system size. Recent studies suggest that some classes of monitored infinite-range systems alleviate this problem by exhibiting a fast saturation of entanglement, resulting in only a polynomial post-selection overhead. This paper answers whether this feature is inherent in infinite-range systems, due to their underlying semiclassical dynamics. We consider three experimentally relevant monitored models: a Tavis-Cummings model, a Superradiance model, and a Bose-Hubbard dimer, each exhibiting nontrivial monitored dynamics. We unveil the occurrence of entanglement phase transitions in these models, showing how the saturation time is strongly affected by bistability regions, which also prevent the mitigation of the post-selection barrier. Finally, we propose experimental realizations of these models, providing a discussion of post selection from an experimental perspective.

DOI
10.1103/physrevresearch.7.023082

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A key challenge in observing measurement-induced phase transitions is the mitigation of the post-selection barrier, which causes the reproducibility of specific sequences of measurement readouts—the trajectory—to be exponentially small in system size. Recent studies suggest that some classes of monitored infinite-range systems alleviate this problem by exhibiting a fast saturation of entanglement, resulting in only a polynomial post-selection overhead. This paper answers whether this feature is inherent in infinite-range systems, due to their underlying semiclassical dynamics. We consider three experimentally relevant monitored models: a Tavis-Cummings model, a Superradiance model, and a Bose-Hubbard dimer, each exhibiting nontrivial monitored dynamics. We unveil the occurrence of entanglement phase transitions in these models, showing how the saturation time is strongly affected by bistability regions, which also prevent the mitigation of the post-selection barrier. Finally, we propose experimental realizations of these models, providing a discussion of post selection from an experimental perspective.
In collective dissipative spin systems, the postselection barrier can be partially mitigated; however, a further obstacle may be posed by the finite temporal resolution of detectors. In this work, we investigate how initial-state inhomogeneities can control waiting-time statistics between quantum jumps, thereby mitigating the detector-resolution problem. We consider a collectively monitored spin model with a boundary time-crystalline phase, introducing inhomogeneity by partitioning the ensemble into two subsystems rotated by an angle θθθ. We find that the measurement-induced phase transition survives under inhomogeneities, with different entanglement scaling regimes. The waiting time increases with θθθ, scaling as 1/N1/N1/N but with a prefactor strongly enhanced by orders of magnitude, and in the anti-aligned limit θ=πθ= πθ=π it remains finite, fully resolving the resolution barrier. This mitigation, however, comes at a cost: the entanglement saturation time becomes significantly longer, partially reintroducing the postselection barrier. Our results highlight a trade-off between detector resolution and postselection overhead, with direct implications for the experimental observation of measurement-induced phenomena.
We study monitored quantum dynamics of infinite-range interacting bosonic systems in the thermodynamic limit. We show that under semiclassical assumptions, the quantum fluctuations along single monitored trajectories adopt a deterministic limit for both quantum-jump and state-diffusion unravelings, and they can be exactly solved. In particular, the hierarchical structure of the equations of motion explains the coincidence of entanglement criticalities and dissipative phase transitions found in previous finite-size numerical studies. We illustrate the findings on a Bose-Hubbard dimer and a collective spin system.
Information-theoretic phase transitions, such as the measurement-induced phase transition (MIPT), characterize the robustness of quantum dynamics to local monitoring and are naturally formulated in terms of trajectories conditioned on typical measurement outcomes, which are naively accessible only through postselection. Here, we implement forced measurements to investigate how explicit postselection alters the nature of the transition. We find that postselection fundamentally alters the universality class by reweighting trajectories that are otherwise rare. In particular, we obtain a correlation-length exponent ν≈2.1ν\approx 2.1ν≈2.1 larger than that of the standard MIPT and a negative effective central charge ceff≈−0.35c_\mathrm{eff}\approx -0.35ceff​≈−0.35. We also compare the postselected MIPT to the entanglement transition of random tensor networks, and demonstrate that their universality class is the same. This setup further allows time-periodic, translationally invariant circuits with postselected weak measurements. In both models, we find that an on-site dimension of at least 3 (qutrits but not qubits) is necessary to induce a transition.
Measurement-induced phases exhibit unconventional dynamics as emergent collective phenomena, yet their behavior in tailored interacting systems - crucial for quantum technologies - remains less understood. We develop a systematic toolbox to analyze monitored dynamics in long-range interacting systems, relevant to platforms like trapped ions and Rydberg atoms. Our method extends spin-wave theory to general dynamical generators at the quantum trajectory level, enabling access to a broader class of states than approaches based on density matrices. This allows efficient simulation of large-scale interacting spins and captures nonlinear dynamical features such as entanglement and trajectory correlations. We showcase the versatility of our framework by exploring entanglement phase transitions in a monitored spin system with power-law interactions in one and two dimensions, where the entanglement scaling changes from logarithm to volume law as the interaction range shortens, and by dwelling on how our method mitigates experimental post-selection challenges in detecting monitored quantum phases.
Recent years have witnessed major progress in the understanding of monitored quantum dynamics, an open quantum setting where the environment is a measurement apparatus that probes the system locally. For the resulting quantum trajectory, unitary evolution and local measurements have competing tendencies in the building of quantum correlations: while the coherent interactions in the former increase the entanglement, the resolving nature of the local measurement collapses the state of the system. Here, the authors study the interplay of monitoring and system dynamics by focusing on the monitored quantum Ising chain as the measurement strength is varied, going from the regime of weak detection, corresponding to the limit of infinite small jumps, to the case of post-selected no-jump case. A sharp transition is found between a logarithmic law phase to an area law phase for the entanglement entropy, which occurs at the same value of the measurement rate in the two limiting situations.
Entanglement phase transitions driven by quantum measurements have emerged as a central paradigm in open quantum many-body physics. Such phase transitions are well established for systems with finite local Hilbert-space dimensions, such as qubits and fermions, while their realization in bosonic systems with unbounded local occupation numbers remains poorly understood. Even in the absence of interactions, number states of bosons are intrinsically non-Gaussian, preventing the use of standard correlation-matrix approaches. To address this problem, we develop a replica-free Keldysh field-theoretic framework that expresses the Renyi entropy of bosonic systems initialized in on-site Fock states in terms of permanents of matrices constructed from single-particle Green's functions. Applying this framework to a continuously monitored one-dimensional cross-stitch lattice conditioned on the no-click trajectory, we uncover a transition from volume-law to logarithmic entanglement scaling. We show that the transition is controlled by a restructuring of the non-Hermitian spectrum that changes the number of long-lived modes from extensive to finite. In the strongly monitored regime, bosons dynamically condense into a microscopic number of slowest-decaying modes, producing logarithmic entanglement scaling, whereas an extensive manifold of long-lived modes at weak monitoring gives rise to volume-law entanglement. Our results establish a distinct mechanism for measurement-induced entanglement transitions in free bosonic systems and provide a computationally efficient diagnostic of the measurement-induced bosonic condensation.