Observation of measurement-induced localization phenomena in a solid-state spin system

Haolin Zhang; Shaoyi Xu; Zihang Zheng; Mengqi Wang; Mingzhe Liu; Zhiyuan Zhao; Ya Wang; Tianyu Xie; Fazhan Shi

AI summary · arXiv: 2610.34262v1 · quant-ph

Observation of measurement-induced localization phenomena in a solid-state spin system

Haolin Zhang, Shaoyi Xu, Zihang Zheng, Mengqi Wang, Mingzhe Liu, Zhiyuan Zhao, Ya Wang, Tianyu Xie,

and 1 more author

Fazhan Shi

Original paper Submitted to arXiv on 25 Oct. 2026 7 pages, 4 figures License: NONEXCLUSIVE-DISTRIB 1.0 Also in: fr

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The essentials

In a diamond ¹³C spin network, projective and global weak measurements prolong spin autocorrelation, providing evidence of measurement-induced localization.

Question

Can measurement suppress thermalization in a many-body spin system governed by its intrinsic dipolar Hamiltonian? The study also asks whether the measured autocorrelation-time increase is associated with the localized regime expected in measurement-induced phase transitions.

Method

The authors measured a target ¹³C spin’s autocorrelation under varying rates of single-spin projective measurements and global weak measurements induced by laser pulses; the network was operationally defined as including approximately 100 spins with appreciable longitudinal coupling. They compared the measurements with Lindblad-equation simulations, using an eight-spin model for autocorrelation and simulations of mutual information for 6, 8, and 10 spins.

Findings

Result Without monitoring, the target spin’s autocorrelation decayed with a characteristic time of 77.9(2.6) ms.
See the passage in the paper
The obtained decay curve (Fig. 1(d)) is well described by a stretched exponential function, yielding a characteristic decay time of 77.9(2.6) ms and a stretching exponent of 0.539(16).
Result Increasing the frequency of projective measurements prolonged the target spin’s autocorrelation time, reaching 1.06 s.
Result Global weak measurements also prolonged autocorrelation at lower measurement frequencies, while at higher frequencies the anti-Zeno effect promoted relaxation.
See the passage in the paper
The results are similar to the projective-measurement case: at low measurement frequencies, faster measurements prolong the spin autocorrelation time; beyond an optimal frequency, the AZE dominates the dynamics and promotes relaxation (Fig. 3(c)).
Authors’ interpretation In simulations, mutual information peaked at a measurement strength interpreted as a crossover to a localized regime, and its crossover coincided with the onset of measured autocorrelation-time enhancement.
See the passage in the paper
Crucially, the onset of the $T_{1}$ enhancement falls within the crossover region extracted from the mutual information simulation, which establishes a direct connection between MIL and the MIPT localized regime in our system: a significant enhancement of $T_{1}$ can serve as an experimental indicator of the localized regime.
Result An eight-spin simulation qualitatively reproduced projective-measurement-induced localization but did not reproduce the experimental double-exponential behavior.
See the passage in the paper
However, the simulations fail to generate the double-exponential behavior in experimental data, possibly owing to the limited spin number.

Limitations

The numerical model includes only eight ¹³C spins, which cannot fully capture the many-body dynamics of the experimental network.
See the passage in the paper
Although eight spins cannot fully capture the many-body dynamics, we select a configuration that most closely matches the experimental data.
The platform does not directly measure entanglement entropy or mutual information, so the link to the localized regime relies on simulations and experimentally accessible autocorrelation.
See the passage in the paper
With such a well-isolated system with intrinsic dipolar interactions, we intend to investigate entanglement structures and transition behaviors, just like circuit-based MIPT experiments [19, 13, 17], but a direct observation of entanglement entropy or mutual information is still beyond the reach of our current platform.

Why it matters

The authors argue that well-isolated diamond ¹³C spins provide a platform for studying measurement-induced many-body dynamics under a physical Hamiltonian rather than random gate sequences. They propose prolonged autocorrelation time as an experimentally accessible indicator of the localized regime, while identifying future entanglement measurements and studies of other phases as goals.

Written by AI from the paper. Passages are checked word for word against the text we analysed; the rest may contain errors.

AI-generated keywords: measurement-induced localization nuclear spins NV center autocorrelation anti-Zeno effect

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Comprehensive Summary
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Original abstract

The paper asks whether repeated quantum measurements can suppress thermalization and preserve local information in a many-body system governed by a physical Hamiltonian, rather than by the gate sequences used in many earlier studies of measurement-induced phase transitions. The authors study a network of carbon-13 nuclear spins surrounding a nitrogen-vacancy (NV) center in diamond. The spins interact through dipolar couplings, while the NV center enables the initialization and readout of a selected nuclear spin and provides a means of applying measurements. First, the team measured the target spin’s unmonitored autocorrelation as it interacted with the surrounding network. The decay followed a stretched exponential, with a characteristic time of 77.9 ± 2.6 milliseconds and a stretching exponent of 0.539 ± 0.016. The researchers then introduced measurements during the spin’s evolution and tracked how long its initial state remained correlated with its later state. In one protocol, they used the NV electron spin and optical pulses to make projective measurements of the target spin. Increasing the measurement frequency generally prolonged the autocorrelation time, to as much as 1.06 seconds. At low measurement frequencies, the decay had two timescales. The authors associate the initial timescale with local equilibration among strongly coupled neighbors and the later one with relaxation involving the wider network. A second protocol used brief laser pulses to weakly measure the network globally. These pulses indirectly probe nuclear spins through their coupling to the NV center. The authors estimate the effective measurement strength at about 0.1 times the pulse repetition frequency. As in the first protocol, increasing the measurement rate initially prolonged the target spin’s autocorrelation. To connect this result to measurement-induced phase transitions, the authors simulated the mutual information between pairs of spins. For the strongly coupled pair they studied, mutual information increased under weak measurement, peaked at a crossover measurement strength, and then declined as measurement became dominant. The experimentally observed onset of autocorrelation enhancement fell within this simulated crossover region, supporting the interpretation that the network had entered a measurement-induced localized regime. However, mutual information was not measured experimentally. The response was not indefinitely monotonic. At sufficiently high measurement frequencies, both protocols showed faster relaxation, attributed to the anti-Zeno effect: repeated NV reinitialization and transverse hyperfine couplings introduce an additional source of single-spin relaxation. In the global-measurement experiment, increased laser-induced polarization of the NV’s zero-spin state also contributed to a modest reduction in autocorrelation at low frequencies. The authors distinguish these effects from measurement-induced suppression of many-body thermalization. Numerical simulations based on a Lindblad master equation reproduced the unmonitored decay and qualitatively captured the localization behavior and several measurement-related effects. The simulations used experimentally determined couplings but were limited to a small cluster of eight nuclear spins selected to represent the experiment; some auxiliary calculations used six, eight, or ten spins. The simulated system could not reproduce the experimentally observed double-exponential decay, and the models required additional assumptions to account for influences from spins outside the simulated cluster. The study presents prolonged spin autocorrelation as an experimentally accessible signature of measurement-induced localization in a well-isolated solid-state spin system. It does not directly demonstrate an entanglement transition: entanglement entropy and mutual information were obtained only in simulations. The finite experimental network, limited simulation size, indirect identification of the localized regime, and high-frequency anti-Zeno effects constrain the strength of the evidence for a full measurement-induced phase transition. The authors propose the platform as a basis for future studies of entanglement and monitored many-body dynamics under intrinsic long-range interactions.

Can Repeated Measurement Keep a Quantum Spin from Forgetting?

In everyday experience, repeatedly checking a system does not usually stop it from changing. Quantum mechanics, however, allows measurement to influence a system’s evolution. The paper “Observation of measurement-induced localization phenomena in a solid-state spin system,” by Haolin Zhang, Shaoyi Xu, Zihang Zheng, Mengqi Wang, Mingzhe Liu, Zhiyuan Zhao et al., explores whether repeated measurements can slow the spread of information through a many-body system and help preserve a spin’s initial state.

Many earlier studies of measurement-induced transitions relied on carefully arranged sequences of quantum gates. This work instead investigates spins interacting through a physical Hamiltonian: the natural dipolar interactions inside a diamond. That makes the experiment a step toward understanding how monitoring affects realistic quantum matter.

A Spin in a Diamond Network

The researchers studied carbon-13 nuclear spins surrounding a nitrogen-vacancy, or NV, center in diamond. These nuclear spins interact with one another through dipolar couplings. The NV center serves as a tool for preparing and reading out a selected nuclear spin, as well as applying measurements during the system’s evolution.

First, the team left the target spin unmonitored and tracked how strongly its later state correlated with its initial state. This autocorrelation decayed in a stretched-exponential pattern, with a characteristic time of 77.9 ± 2.6 milliseconds and a stretching exponent of 0.539 ± 0.016. In practical terms, the surrounding spins gradually caused the target spin to lose memory of where it began.

Projective Measurements Slow the Loss of Memory

The first measurement protocol used the NV electron spin and optical pulses to make projective measurements of the target nuclear spin. The team then varied how frequently those measurements occurred. In general, measuring more often prolonged the time over which the target spin remained correlated with its initial state. At the longest reported times, the autocorrelation persisted for as much as 1.06 seconds—far beyond the unmonitored characteristic time.

At low measurement frequencies, the decay showed two timescales. The researchers associate the faster initial process with local equilibration among strongly coupled neighboring spins. The slower stage may reflect relaxation involving a larger portion of the spin network. This distinction suggests that measurements can affect not just how quickly information fades, but also which parts of the network are involved in its spread.

Weakly Measuring the Wider Network

A second protocol used brief laser pulses to probe the network more globally. The pulses indirectly measure nuclear spins through their coupling to the NV center. The researchers estimated the effective measurement strength to be about 0.1 times the pulse repetition frequency.

As in the projective-measurement protocol, raising the measurement rate initially increased the target spin’s autocorrelation time. The result is consistent with measurement suppressing the system’s tendency to thermalize—that is, slowing the process by which interactions spread information and erase local memory.

What the Simulations Add—and What They Do Not

To connect the observations to measurement-induced phase transitions, the team simulated mutual information between pairs of spins. For the strongly coupled pair considered, mutual information rose under weak measurement, reached a peak at a crossover measurement strength, and then fell as measurement became dominant. The experimentally observed onset of stronger autocorrelation fell within this simulated crossover region, supporting the interpretation that the system entered a measurement-induced localized regime.

There is an important qualification: mutual information was not measured in the experiment. The simulation therefore provides a theoretical link between the observed persistence of spin memory and the proposed localization picture, rather than a direct experimental observation of the transition. The study does not directly demonstrate an entanglement transition either; entanglement entropy and mutual information were calculated only in simulations.

The models used experimentally determined couplings but included only small clusters of six, eight, or ten nuclear spins. These simulations reproduced the unmonitored decay and captured aspects of the localization behavior, but they could not reproduce the observed double-exponential decay. The researchers also needed additional assumptions to account for influences from spins beyond the simulated cluster.

Why Measuring More Is Not Always Better

The slowing of autocorrelation did not continue indefinitely. At sufficiently high measurement frequencies, both protocols showed faster relaxation. The authors attribute this reversal to an anti-Zeno effect: repeated NV reinitialization and transverse hyperfine couplings introduce an additional source of single-spin relaxation.

In the global-measurement experiment, stronger laser-induced polarization of the NV’s zero-spin state also contributed to a modest reduction in autocorrelation at low frequencies. These effects complicate the picture, but the authors distinguish them from the suppression of many-body thermalization associated with measurement-induced localization.

A Useful Platform, with Open Questions

The central result is that repeated measurements can prolong the memory of a nuclear spin embedded in a naturally interacting solid-state network. This makes autocorrelation a practical experimental signal for studying measurement-induced localization in a well-isolated spin system.

The findings are promising but not definitive evidence for a full measurement-induced phase transition. The experimental network is finite, the simulations capture only small clusters, and the identification of localization is indirect. Future work could use this platform to probe entanglement and monitored many-body dynamics more directly, while exploring how measurement reshapes systems governed by intrinsic long-range interactions.

Created on 03 Nov. 2026

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Observation of measurement-induced localization phenomena in a solid-state spin system

The essentials

Question

Method

Findings

Limitations

Why it matters

Read further

Definitions

Can Repeated Measurement Keep a Quantum Spin from Forgetting?

A Spin in a Diamond Network

Projective Measurements Slow the Loss of Memory

Weakly Measuring the Wider Network

What the Simulations Add—and What They Do Not

Why Measuring More Is Not Always Better

A Useful Platform, with Open Questions

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