Observation of measurement-induced localization phenomena in a solid-state spin system
Authors: Haolin Zhang, Shaoyi Xu, Zihang Zheng, Mengqi Wang, Mingzhe Liu, Zhiyuan Zhao, Ya Wang, Tianyu Xie, Fazhan Shi
Abstract
Quantum measurement can profoundly impact the dynamics of many-body systems, for instance, inducing phase transitions from volume-law chaotic phases to area-law localized phases. While chaotic phases emerge naturally in generic many-body systems, the experimental realization of a fully localized phase driven by measurement remains challenging, primarily owing to the stringent requirement of near-perfect isolation of the system from environmental dissipation. Here we experimentally observe measurement-induced localization phenomena in an interacting $^{13}\mathrm{C}$ nuclear spin system in diamond. In contrast to previous circuit-model-based experiments, our well-isolated system evolves under a physical many-body Hamiltonian with measurements intervening at intervals. By implementing either projective measurements on a single spin or global weak measurements on the entire system, we observe substantially prolonged spin autocorrelation times as the measurement frequency increases. Our results, combined with numerical simulations, provide evidence that quantum measurement can drive a many-body system into a localized regime, and lay the groundwork for future experimental investigations into measurement-induced many-body dynamics and related entanglement phenomena.
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Closest papers
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Nonlinear collective-spin dynamics for quantum-enhanced sensing in solid-state platformsLe-Bin Ho · 2026 · Materials for Quantum Technology · Not summarized yet
Abstract
Collective spin systems in solid-state materials are promising platforms for quantum-enhanced sensing. In systems such as nitrogen-vacancy centers in diamond, donor spins in silicon, and magnetic materials, interactions among many spins can generate collective quantum correlations that improve measurement precision beyond the standard quantum limit. This tutorial develops an intuitive, materials-oriented framework for understanding these effects through nonlinear collective-spin dynamics. We show how nonlinear interactions reshape collective spin states in phase space, redistribute quantum fluctuations, and generate metrologically useful states such as spin-squeezed and entangled states. We …
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Measurement-induced entanglement phase transition on a superconducting quantum processor with mid-circuit readoutJin Ming Koh, Shi-Ning Sun, M. Motta et al. · 2022 · Nature Physics · cited 239 times · Not summarized yet
This experiment observes an entanglement phase transition in a hybrid random circuit on superconducting qubits, rather than localization in a dipolar spin system.
Abstract
Quantum many-body systems subjected to unitary evolution with the addition of interspersed measurements exhibit a variety of dynamical phases that do not occur under pure unitary evolution. However, these systems remain challenging to investigate on near-term quantum hardware owing to the need for numerous ancilla qubits or repeated high-fidelity mid-circuit measurements, a capability that has only recently become available. Here we report the realization of a measurement-induced entanglement phase transition with a hybrid random circuit on up to 14 superconducting qubits with mid-circuit readout capability. We directly observe extensive and sub-extensive scaling of entanglement entropy in t…
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Direct Observation of Dipolar-Driven Anisotropic Quantum Projection Noise in a Solid-State Spin EnsembleTasuku Ono, Wei-Jie Wu, Hao-Pu Yang et al. · 2026 · Not summarized yet
Abstract
The nitrogen-vacancy (NV) center in diamond is a prominent quantum-sensing platform. Combining readout at the quantum projection noise limit with strong dipolar interactions promises substantial gains in sensitivity. However, experimentally accessing this regime has remained a longstanding challenge. In this work, we demonstrate quantum-projection-noise-resolved readout of a strongly-interacting, two-dimensional ensemble of NV centers. Our approach leverages repetitive readout via the NV's intrinsic $^{15}$N nuclear memory at a moderate magnetic field ($\sim 0.3$ T), improving the readout fidelities by nearly an order of magnitude. This enables us to directly resolve the quantum projection n…
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Measurement-induced criticality in (2+1) -dimensional hybrid quantum circuitsX. Turkeshi, R. Fazio, M. Dalmonte · 2020 · Physical Review B · cited 146 times · Not summarized yet
This numerical study analyzes measurement-driven entanglement transitions in two-dimensional spin circuits, the broader transition framework motivating the spin-system experiment.
Abstract
We investigate the dynamics of two-dimensional quantum spin systems under the combined effect of random unitary gates and local projective measurements. When considering steady states, a measurement-induced transition occurs between two distinct dynamical phases, one characterized by a volume-law scaling of entanglement entropy, the other by an area law. Employing stabilizer states and Clifford random unitary gates, we numerically investigate square lattices of linear dimension up to $L=48$ for two distinct measurement protocols. For both protocols, we observe a transition point where the dominant contribution in the entanglement entropy displays multiplicative logarithmic violations to the …
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Critical Thermalization of a Disordered Dipolar Spin System in Diamond.G. Kucsko, Soonwon Choi, Joonhee Choi et al. · 2016 · Physical Review Letters · cited 163 times · Not summarized yet
This study measures slow thermalization in disordered dipolar spins in diamond, addressing relaxation in a related solid-state spin system without measurement-driven localization.
Abstract
Statistical mechanics underlies our understanding of macroscopic quantum systems. It is based on the assumption that out-of-equilibrium systems rapidly approach their equilibrium states, forgetting any information about their microscopic initial conditions. This fundamental paradigm is challenged by disordered systems, in which a slowdown or even absence of thermalization is expected. We report the observation of critical thermalization in a three dimensional ensemble of ∼10^{6} electronic spins coupled via dipolar interactions. By controlling the spin states of nitrogen vacancy color centers in diamond, we observe slow, subexponential relaxation dynamics and identify a regime of power-law d…
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Depolarization Dynamics in a Strongly Interacting Solid-State Spin Ensemble.Joonhee Choi, Soonwon Choi, G. Kucsko et al. · 2016 · Physical Review Letters · cited 119 times · Not summarized yet
This study models depolarization in dipolar-interacting diamond spins, examining spin relaxation rather than measurement-induced localization.
Abstract
We study the depolarization dynamics of a dense ensemble of dipolar interacting spins, associated with nitrogen-vacancy centers in diamond. We observe anomalously fast, density-dependent, and nonexponential spin relaxation. To explain these observations, we propose a microscopic model where an interplay of long-range interactions, disorder, and dissipation leads to predictions that are in quantitative agreement with both current and prior experimental results. Our results pave the way for controlled many-body experiments with long-lived and strongly interacting ensembles of solid-state spins.
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Measurement-induced entanglement and teleportation on a noisy quantum processorJ. C. Hoke, M. Ippoliti, E. Rosenberg et al. · 2023 · Nature · cited 221 times · Not summarized yet
This experiment studies measurement-induced entanglement and teleportation on a noisy processor, whereas the paper probes localization through spin autocorrelation.
Abstract
Measurement has a special role in quantum theory^ 1 : by collapsing the wavefunction, it can enable phenomena such as teleportation^ 2 and thereby alter the ‘arrow of time’ that constrains unitary evolution. When integrated in many-body dynamics, measurements can lead to emergent patterns of quantum information in space–time^ 3 – 10 that go beyond the established paradigms for characterizing phases, either in or out of equilibrium^ 11 – 13 . For present-day noisy intermediate-scale quantum (NISQ) processors^ 14 , the experimental realization of such physics can be problematic because of hardware limitations and the stochastic nature of quantum measurement. Here we address these experimental …
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Measurement-Only Dynamical Phase Transitions in Spin-1 ChainsKemal Aziz, Hai-Ning Pan, J. Pixley · 2026 · Not summarized yet
Abstract
We study measurement-only dynamics in an interacting spin-1 chain, using forced, normalized local projections rather than Born-rule-sampled measurement outcomes. Starting from the nearest-neighbor (NN) Affleck-Kennedy-Lieb-Tasaki (AKLT) Haldane symmetry-protected topological state, we show that competing local projectors drive this order toward three distinct dynamical phases: a featureless topologically trivial product state, an explicitly dimerized valence-bond-solid state, and a topologically trivial next-nearest-neighbor (NNN) AKLT state consisting of two interwoven Haldane chains. Using matrix product state and exact statevector simulations, we identify continuous transitions among thes…
Prior work it builds on
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Experimental Demonstration of Scalable Cross-Entropy Benchmarking to Detect Measurement-Induced Phase Transitions on a Superconducting Quantum Processor.Hirsh Kamakari, Jia-Ce Sun, Yao-Dong Li et al. · 2024 · Physical Review Letters · cited 37 times · Not summarized yet
This study tests cross-entropy benchmarking as a scalable detector of measurement-induced transitions, rather than using spin autocorrelation to identify localization.
Abstract
Quantum systems subject to random unitary evolution and measurements at random points in spacetime exhibit entanglement phase transitions which depend on the frequency of these measurements. Past work has experimentally observed entanglement phase transitions on near-term quantum computers, but the characterization approach using entanglement entropy is not scalable due to exponential overhead of quantum state tomography and postselection. Recently, an alternative protocol to detect entanglement phase transitions using linear cross entropy was proposed, attempting to eliminate both bottlenecks. Here, we report demonstrations of this protocol in systems with one-dimensional and all-to-all con…
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Controlling Local Thermalization Dynamics in a Floquet-Engineered Dipolar Ensemble.L. Martin, Heng-Yun Zhou, Nathaniel T. Leitao et al. · 2022 · Physical Review Letters · cited 27 times · Not summarized yet
Abstract
Understanding the microscopic mechanisms of thermalization in closed quantum systems is among the key challenges in modern quantum many-body physics. We demonstrate a method to probe local thermalization in a large-scale many-body system by exploiting its inherent disorder and use this to uncover the thermalization mechanisms in a three-dimensional, dipolar-interacting spin system with tunable interactions. Utilizing advanced Hamiltonian engineering techniques to explore a range of spin Hamiltonians, we observe a striking change in the characteristic shape and timescale of local correlation decay as we vary the engineered exchange anisotropy. We show that these observations originate from th…
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Measurement-Induced Localization of an Ultracold Lattice Gas.S. Chakram, Y. Patil, M. Vengalattore · 2015 · Physical Review Letters · cited 154 times · Not summarized yet
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Measurement-induced quantum criticality under continuous monitoringY. Fuji, Y. Ashida · 2020 · Physical Review B · cited 157 times · Not summarized yet
Abstract
We investigate entanglement phase transitions from volume-law to area-law entanglement in a quantum many-body state under continuous position measurement on the basis of the quantum trajectory approach. We find the signatures of the transitions as peak structures in the mutual information as a function of measurement strength, as previously reported for random unitary circuits with projective measurements. At the transition points, the entanglement entropy scales logarithmically and various physical quantities scale algebraically, implying emergent conformal criticality, for both integrable and nonintegrable one-dimensional interacting Hamiltonians; however, such transitions have been argued…
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Observation of discrete time-crystalline order in a disordered dipolar many-body systemSoonwon Choi, Joonhee Choi, R. Landig et al. · 2016 · Nature · cited 945 times · Not summarized yet
Abstract
Understanding quantum dynamics away from equilibrium is an outstanding challenge in the modern physical sciences. Out-of-equilibrium systems can display a rich variety of phenomena, including self-organized synchronization and dynamical phase transitions. More recently, advances in the controlled manipulation of isolated many-body systems have enabled detailed studies of non-equilibrium phases in strongly interacting quantum matter; for example, the interplay between periodic driving, disorder and strong interactions has been predicted to result in exotic ‘time-crystalline’ phases, in which a system exhibits temporal correlations at integer multiples of the fundamental driving period, breaki…
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Updated on 3 November 2026.