Repeated observation does more than disturb a quantum system. In many-body systems, measurement can compete with entanglement strongly enough to drive an entirely new kind of phase transition.
Quantum measurement is often introduced as an interruption. A quantum state evolves smoothly according to Schrödinger’s equation until a measurement is performed, at which point the state is projected onto an outcome. In that textbook picture, unitary evolution creates superpositions and entanglement, while measurement destroys some of that quantum uncertainty by extracting information. For many decades these processes were usually studied separately. Modern many-body physics has revealed that when unitary evolution and measurement occur repeatedly inside the same interacting system, their competition can itself organize the quantum state into distinct phases. Instead of temperature, magnetic field, pressure, or interaction strength controlling the transition, the tuning parameter can simply be how frequently the system is observed.
These measurement-induced phase transitions, or MIPTs, are unusual because the transition does not primarily concern energy, magnetization, particle density, or another conventional local observable. It concerns the architecture of quantum information inside the many-body wave function. At low measurement rates, unitary dynamics can spread entanglement faster than measurements remove it, producing a highly entangled phase. At sufficiently high measurement rates, repeated observations continually cut apart that entanglement, producing a weakly entangled phase closely related to the quantum Zeno effect. Between them lies a genuine critical point separating two fundamentally different ways in which information can be distributed through a quantum system.
A useful theoretical model is a hybrid quantum circuit. Consider a chain of $L$ qubits. Between measurements, pairs of qubits undergo entangling unitary gates $U_t$. At random spacetime locations, individual qubits are projectively measured with probability $p$. For a particular measurement outcome $m$, it is useful to separate the Born probability from the normalized state update. If the state immediately before the step is $|\psi(t)\rangle$, the probability of obtaining outcome $m$ is
$$ p_m = \langle \psi(t) | U_t^\dagger M_m^\dagger M_m U_t | \psi(t) \rangle $$
After that outcome is obtained, the normalized state becomes
$$ |\psi_m(t+1)\rangle = \frac{M_m U_t |\psi(t)\rangle}{\sqrt{p_m}} $$
Here $M_m$ is the measurement operator associated with the observed outcome, while $p_m$ is its Born probability. Repeating this process produces a stochastic quantum trajectory whose evolution depends on the complete measurement record. Unlike the deterministic unitary evolution of a closed quantum system, conditioned monitored dynamics combine coherent evolution with probabilistic state updates.
The two ingredients push the wave function in opposite directions. Generic interacting unitary gates scramble information across many qubits. A local perturbation that initially affects one site spreads through increasingly nonlocal operators, while entanglement grows between distant regions. Measurements act differently. Measuring one qubit reveals information about that degree of freedom to the outside observer and projects part of the many-body state, locally suppressing quantum uncertainty.
The measurement-induced transition arises because neither process necessarily wins immediately. Sparse measurements can be absorbed into a sufficiently strongly scrambling state, while dense measurements can prevent long-range entanglement from ever becoming established. The result is not merely a gradual reduction of entanglement. In the thermodynamic limit, suitable monitored circuits exhibit a sharp transition at a critical measurement probability $p_c$ separating two distinct organizations of quantum information.
The natural quantity for distinguishing these phases is entanglement entropy. Divide the system into a region $A$ and the remainder $B$. For a pure many-body state $|\psi\rangle$, the reduced density matrix of region $A$ is obtained by tracing over $B$:
$$ \rho_A = \mathrm{Tr}_B(|\psi\rangle\langle\psi|) $$
The corresponding von Neumann entanglement entropy is
$$ S_A = -\mathrm{Tr}(\rho_A \ln \rho_A) $$
If $A$ is completely unentangled with the rest of the system, $\rho_A$ is pure and $S_A=0$. If information about $A$ is distributed through quantum correlations with $B$, the reduced state is mixed and $S_A$ becomes positive. Entanglement entropy therefore quantifies how much quantum information is shared across the partition.
In a one-dimensional monitored circuit, the two phases display radically different scaling. Below the critical measurement rate, the long-time state typically obeys a volume law:
$$ S_A \sim s(p)|A| \qquad p<p_c $$
Here $|A|$ is the number of qubits in the subsystem and $s(p)$ is an entanglement-entropy density. The entropy therefore grows extensively with subsystem size, indicating that information within $A$ is strongly correlated with degrees of freedom distributed throughout the rest of the system.
Above the transition, repeated measurements instead produce an area-law state:
$$ S_A = O(1) \qquad p>p_c $$
For a contiguous interval in one dimension, the boundary contains only a fixed number of endpoints, so an area law means that the entanglement remains of order unity even as the interval becomes longer. At the critical measurement rate, many monitored circuit models instead exhibit approximately logarithmic scaling,
$$ S_A \sim \alpha \ln |A| $$
where $\alpha$ is a critical coefficient whose value depends on the universality class.
This distinction is remarkable because the microscopic circuits on either side of the transition can look almost identical. The same kinds of gates may be applied, the same observables measured, and no conventional equilibrium Hamiltonian phase transition is required. What changes is the global scaling structure of entanglement.
The strongly measured regime can be connected to the quantum Zeno effect. If an unstable quantum state is measured sufficiently frequently in the basis that distinguishes whether it has changed, the measurements can inhibit its evolution. In monitored many-body systems, the idea generalizes. Frequent local measurements repeatedly collapse degrees of freedom before coherent interactions have enough time to build large-scale entanglement. Li, Chen, and Fisher explicitly identified this competition in 2018, finding a weak-measurement volume-law phase and a strongly monitored “quantum Zeno phase” separated by a continuous entanglement transition.
It would nevertheless be misleading to describe the low-measurement phase simply as a state in which measurement has little effect. Individual measurements still collapse local observables. What survives is not every microscopic superposition but the global encoding of quantum information. Scrambling distributes information so nonlocally that measuring a limited number of individual qubits may reveal too little to destroy the encoded many-body correlations. This is why measurement-induced transitions became closely connected to quantum error correction. In the entangling phase, information about an initially encoded quantum degree of freedom can become hidden throughout the many-body state in a manner that resembles a dynamically generated error-correcting code. Local measurements remove physical degrees of freedom, but below a threshold the global information can remain recoverable. Choi, Bao, Qi, and Altman made this connection explicit by showing that the transition can be interpreted as a competition between scrambling-generated encoding and measurement-induced information loss.
The analogy is structurally close to fault tolerance. In a conventional quantum code, logical information is distributed across many physical qubits so that erasing some of them does not immediately erase the logical state. In a monitored chaotic circuit, unitary dynamics continuously scrambles the information into nonlocal correlations, while measurements continuously attempt to extract pieces of it. The critical measurement rate behaves like an information-theoretic threshold separating a regime where encoded information survives from one where the measurement record becomes powerful enough to reveal and destroy it.
This viewpoint leads to a particularly deep interpretation of the transition. The outside observer accumulates a classical record containing every measurement outcome,
$$ \mathbf{m}=(m_1,m_2,\ldots,m_N) $$
and the conditioned quantum state depends on that record. At low measurement rates, $\mathbf{m}$ does not contain enough information to reconstruct the full hidden quantum state. Much of the information remains encoded nonlocally in correlations among unmeasured degrees of freedom. At high measurement rates, the accumulated record becomes sufficiently informative that the remaining quantum state can purify much more rapidly from the observer's perspective. This motivates related purification, learnability, and decodability transitions in monitored quantum dynamics. Experiments with trapped ions have directly explored measurement-induced purification, while later theoretical work has connected monitored dynamics to quantum inference problems in which an observer attempts to infer hidden quantum information from the measurement stream.
This is unusual because observation is no longer merely something performed after the physics has occurred. Measurement helps determine the information structure of the evolving state itself. The apparatus participates in deciding whether quantum information remains hidden in nonlocal correlations or becomes accessible through the classical record. In this sense, monitored many-body physics turns the familiar measurement problem into something statistical: instead of asking only what one measurement does to one particle, it asks how an extensive pattern of measurements reorganizes the information structure of an interacting quantum system.
One of the most surprising features of measurement-induced phase transitions is that the transition can be invisible to ordinary averaged observables. If the individual measurement outcomes are discarded and one averages over all possible trajectories, the density matrix evolves through a quantum channel. For one unitary step followed by measurement, this can be written as
$$ \rho'=\sum_m M_mU\rho U^\dagger M_m^\dagger $$
where the measurement operators satisfy
$$ \sum_m M_m^\dagger M_m=I $$
The measurement-induced entanglement transition generally appears in nonlinear properties of individual conditioned trajectories, rather than simply in ordinary expectation values calculated from the averaged density matrix. A conventional observable has an expectation value of the form
$$ \langle O\rangle=\mathrm{Tr}(\rho O) $$
and quantities of this type can remain smooth even while the trajectory entanglement undergoes a sharp transition. This is why a system can cross a measurement-induced entanglement transition without displaying an equally sharp change in a local observable such as magnetization or particle density. The transition is encoded in how quantum information is distributed across individual measurement histories, information that can disappear when all trajectories are averaged together.
This feature also creates one of the largest experimental obstacles in the field. Suppose a circuit contains $N_m$ binary measurements. In a sufficiently random circuit, one particular sequence of outcomes can occur with a probability on the scale of
$$ P_{\mathrm{traj}}\sim2^{-N_m} $$
As $N_m$ increases, reproducing one exact measurement trajectory by repeatedly running the experiment and waiting for the same sequence of outcomes can therefore require an exponentially growing number of trials. This is the postselection barrier.
Directly measuring entanglement entropy creates an additional difficulty because generic quantum-state tomography also becomes exponentially expensive as the number of qubits increases. Measurement-induced transitions are therefore naturally defined using precisely the nonlinear information quantities that become hardest to reconstruct in large systems. Overcoming this tension has turned experimental access to MIPTs into a problem in quantum-information theory rather than simply a question of improving hardware fidelity.
Despite this difficulty, experiments have progressively reached the transition. In 2022, researchers used a trapped-ion quantum computer to explore measurement-induced purification phases in random circuits. In 2023, a superconducting processor with mid-circuit readout implemented hybrid random circuits on up to 14 qubits and directly observed the crossover between extensive and sub-extensive entanglement scaling as the measurement rate was varied. The experiment also obtained finite-size critical scaling consistent with a measurement-induced transition.
A separate 2023 experiment studied measurement-induced information phases using as many as 70 superconducting qubits. Rather than implementing the monitored dynamics in the most literal way, the researchers used a space-time duality that exchanged aspects of space and time in the circuit, allowing them to access entanglement scaling and measurement-induced teleportation without requiring the same pattern of mid-circuit measurements. The observed phases exhibited sharply different responses to noise, providing another operational signature of the underlying information transition.
The teleportation connection is especially interesting. Measurement normally appears to destroy quantum information, yet measurements can also redirect entanglement and enable information to emerge elsewhere. In the appropriate monitored phase, measurement outcomes combined with pre-existing many-body entanglement can establish long-range quantum channels. Measurement is therefore neither inherently entangling nor inherently disentangling. Its effect depends on the quantum information already distributed through the system and on how the outcomes are used.
The postselection problem has become a central target in more recent work. A theoretically proposed linear cross-entropy diagnostic compares measurement-outcome probability distributions from related circuits and can distinguish the phases without reconstructing the complete wave function. In 2025, this strategy was demonstrated experimentally on superconducting hardware with systems of up to 22 qubits, substantially extending the regime accessible without conventional postselection. The resulting data exhibited finite-size scaling and critical exponents in semiquantitative agreement with theoretical expectations.
In 2026, researchers reported another important step: a postselection-free observation of an MIPT using universal gates in a tree-shaped quantum circuit implemented on a trapped-ion computer. The tree geometry was not just a convenient layout. It allowed the measurement record to be decoded with computational effort growing only linearly with the number of qubits, rather than exponentially. The experiment realized an entangling-disentangling transition using Haar-random unitary operations and found agreement with an analytically tractable theory without requiring error mitigation.
That result points toward an important shift in the field. The question is increasingly not whether measurement-induced phases exist, but how to probe them in systems too large and too generic for brute-force classical reconstruction. A genuine many-body phase should ultimately be characterizable without requiring a classical computer to simulate every microscopic quantum trajectory first.
Theoretical work has also revealed that measurement-induced criticality is closely related to classical statistical mechanics in spacetime. In certain simplified monitored circuits, entanglement can be mapped onto geometric optimization problems. Skinner, Ruhman, and Nahum showed that a toy model based on the zeroth Rényi entropy maps exactly onto classical percolation. In this picture, unitary gates build connections through circuit spacetime while measurements effectively cut those connections. The entanglement of a final subsystem can then be related to a minimal path or membrane passing through the resulting disordered spacetime geometry.
A broader family of entanglement measures is given by the Rényi entropies,
$$ S_A^{(n)}=\frac{1}{1-n}\ln\mathrm{Tr}(\rho_A^n) $$
where $n$ is the Rényi index. In the limit $n\to1$, this expression approaches the von Neumann entropy,
$$ \lim_{n\to1}S_A^{(n)}=S_A $$
The replica method studies these quantities by introducing multiple copies of the monitored circuit and converting averaged entanglement calculations into effective statistical-mechanical partition functions. The measurement-induced critical point can then appear as an ordering transition of emergent replica degrees of freedom. The precise universality class depends on the circuit ensemble, dimensionality, symmetries, conservation laws, and the entanglement quantity being studied, so generic MIPTs should not simply be identified with ordinary percolation. Nevertheless, these mappings explain why measurement-induced transitions exhibit familiar signatures of continuous critical phenomena, including diverging correlation lengths and finite-size scaling, even though the quantity undergoing the transition is quantum entanglement rather than a conventional thermodynamic order parameter.
Near the critical measurement probability $p_c$, the characteristic correlation length is expected to diverge as
$$ \xi\sim|p-p_c|^{-\nu} $$
where $\nu$ is the correlation-length critical exponent. A finite system of length $L$ cannot display a true divergence, so observables instead depend on a dimensionless finite-size scaling variable such as
$$ x=(p-p_c)L^{1/\nu} $$
Measurements performed at different system sizes can therefore be rescaled and compared through a common scaling function. If the correct values of $p_c$ and $\nu$ are chosen, data from different values of $L$ can collapse onto the same universal curve. This is the same mathematical logic used to identify equilibrium critical points, now applied to the geometry and flow of quantum information through circuit spacetime. Experimental data-collapse analyses on superconducting quantum processors have already used this framework to locate and characterize measurement-induced criticality.
The resemblance to statistical mechanics is not merely mathematical decoration. It suggests that quantum information itself can exhibit universality. Microscopic details of individual gates may become irrelevant near criticality, just as the microscopic chemistry of water is not required to understand every universal property near a liquid-gas critical point. Very different monitored systems can flow toward the same long-distance description if they share dimensionality, symmetries, conservation laws, and the relevant information-theoretic structure.
At the same time, measurement introduces possibilities unavailable in equilibrium matter. Conserved quantities can undergo separate charge-sharpening or learnability transitions. Feedback conditioned on measurement outcomes can create phases that would not occur under passive monitoring. Long-range interactions can alter the scaling of entanglement. Continuous weak measurements interpolate between smooth stochastic evolution and projective circuits, while non-Hermitian descriptions can emerge when one conditions on particular measurement records. The MIPT is therefore best understood not as one isolated critical point but as the entrance to a much larger theory of monitored quantum matter.
There is also a conceptual connection to black-hole information and holography. Random quantum circuits are widely used as simplified models of scrambling because they rapidly distribute initially local information into highly nonlocal correlations. In a black-hole analogy, the unitary dynamics resemble the scrambling of information inside a chaotic quantum system, while measurements resemble information leaking into an environment. Whether the original quantum information remains protected inside inaccessible correlations or becomes recoverable from the emitted record is structurally similar to questions that arise in quantum error correction and holographic descriptions of gravity. The connection should not be overstated: a monitored circuit is not literally a black hole. But the same mathematical language of entanglement, decoding, scrambling, and information recovery appears across these problems.
This is one reason MIPTs have attracted researchers from condensed-matter physics, quantum information, statistical mechanics, and quantum gravity. They provide unusually simple laboratory models in which questions about the location and recoverability of quantum information become genuine phase-transition problems. Instead of asking vaguely whether information is “lost,” one can define an order parameter, vary a control parameter, extract critical exponents, and identify the threshold where the answer changes.
The deepest lesson of measurement-induced criticality is that observation and entanglement are competing dynamical resources. Unitary quantum mechanics continually hides local information by spreading it into increasingly complex correlations. Measurement continually converts part of that hidden quantum information into explicit classical information available to an observer. At low measurement rates, the many-body state can protect quantum information faster than the environment extracts it. At high rates, the observer wins. At the critical point, neither process establishes a characteristic scale, and the structure of entanglement becomes scale invariant.
This forces a broader view of what constitutes a phase of matter. Traditional phases describe how particles arrange, which symmetries are broken, or which topological invariants characterize a ground state. Measurement-induced phases describe something different: how information is organized in the history of a quantum system. Two circuits can have similar local densities, similar energies, and even similar averaged density matrices while belonging to different entanglement phases because their individual quantum trajectories distribute information in fundamentally different ways.
Measurement therefore does more than reveal a quantum state, and it does more than destroy one. When applied repeatedly across an interacting system, it becomes a control parameter capable of restructuring the entire many-body wave function. The boundary between the resulting phases is not written in the positions of particles or the orientation of spins. It is written in which parts of the universe must be known before the state of one small part can be predicted.
In monitored quantum matter, the act of learning about the system changes the phase in which its information lives.