Quantum critical systems constitute appealing platforms for exploring novel measurement-induced phenomena due to their innate sensitivity to perturbations.We study the impact of measurements on paradigmatic Ising quantum-critical chains using an explicit protocol, whereby correlated ancillae are entangled with the critical chain and then projectively measured.Using a perturbative analytic framework supported by extensive numerical simulations, we demonstrate that measurements can qualitatively alter critical correlations in a manner dependent on the choice of entangling gate, ancilla measurement basis, measurement outcome, and nature of ancilla correlations.We further show that measurement-altered Ising criticality can be pursued surprisingly efficiently in experiments featuring of order 100 qubits by postselecting for high-probability measurement outcomes or, in certain cases, by averaging observables separately over measurement outcomes residing in distinct symmetry sectors.Our framework naturally adapts to more exotic quantum-critical points and highlights opportunities for realization in noisy intermediate-scale quantum hardware and in Rydberg arrays.
Quantum critical systems constitute appealing platforms for exploring novel measurement-induced phenomena due to their innate sensitivity to perturbations.We study the impact of measurements on paradigmatic Ising quantum-critical chains using an explicit protocol, whereby correlated ancillae are entangled with the critical chain and then projectively measured.Using a perturbative analytic framework supported by extensive numerical simulations, we demonstrate that measurements can qualitatively alter critical correlations in a manner dependent on the choice of entangling gate, ancilla measurement basis, measurement outcome, and nature of ancilla correlations.We further show that measurement-altered Ising criticality can be pursued surprisingly efficiently in experiments featuring of order 100 qubits by postselecting for high-probability measurement outcomes or, in certain cases, by averaging observables separately over measurement outcomes residing in distinct symmetry sectors.Our framework naturally adapts to more exotic quantum-critical points and highlights opportunities for realization in noisy intermediate-scale quantum hardware and in Rydberg arrays.
Weak measurements have been predicted to dramatically alter universal properties of quantum critical wave functions, though experimental validation remains an open problem. Here we devise a practical scheme for realizing measurement-altered criticality in a chain of Rydberg atoms tuned to Ising and tricritical Ising phase transitions. In particular, we show that projectively measuring a periodic subset of atoms alters quantum critical correlations in distinct ways that one can control via the choice of measured sites and the measurement outcomes. While our protocol relies on postselection, the measurement outcomes yielding the most dramatic consequences occur with surprisingly large probabilities: O(10%) with chains featuring O(100) sites. Characterizing the proposed postmeasurement states requires only an adjustment in the post-process averaging of outcomes used to characterize unmeasured critical states, resulting in minimal additional experimental overhead for demonstrating measurement-altered criticality.
Measurements are usually introduced as probes of quantum systems, but they can also act as a powerful, intrinsically nonunitary control knob for manipulating quantum states. This thesis develops the theory, experimental realization, and detection of measurement-altered quantum criticality in one-dimension: the phenomenon where local measurements on critical wave functions reshape universal long-distance correlations, entanglement, and other scaling behaviors. We show that measurements generate defect or boundary perturbations in the underlying conformal field theory, producing new measurement-induced fixed points and new universal observables that are often invisible to the pristine theory. In transverse-field Ising chains, we design measurement-altered criticality protocols in which correlated ancillas are entangled with the critical system and then projectively measured. This setting shows that measurement basis, entangling gate, measurement outcome, and ancilla correlations can qualitatively change correlations in the system and induce outcome-dependent order-parameter condensation. We also develop nonstandard probes --- including higher moments and symmetry-resolved averages --- that retain nontrivial signatures of the post-measurement ensemble. These ideas are then connected to quantum information by studying imperfect teleportation of critical many-body wavefunctions. Teleportation errors can be reinterpreted as effective weak measurements acting on an otherwise faithfully teleported critical state. This perspective yields a classification of protocols in which imperfections either preserve universal correlations and entanglement scaling, continuously deform them, or destroy long-range entanglement while leaving altered power-law correlations behind. Measurement-altered criticality therefore becomes not only a fundamental phenomenon, but also a tool for understanding and optimizing noisy quantum-information protocols. We also broaden the framework to measurement-induced boundary physics. In a gapless parent of the one-dimensional cluster state, a single round of measurements can generate boundary conformal field theories with distinct universal properties. Rotating the measurement basis drives transitions between these boundary fixed points, producing measurement-induced boundary transitions that have no analogue in the descendant gapped cluster state. Extensions to tricritical Ising and three-state Potts criticality show that such transitions arise generally in 1+1D conformal field theories. Finally, the thesis addresses experimental access. We propose practical protocols for observing measurement-altered criticality in Rydberg atom arrays tuned to Ising and tricritical-Ising transitions, where projective measurements of selected atoms can controllably modify critical correlations with experimentally favorable post-selection probabilities. We also develop a post-selection-free framework for extracting nonlinear observables from raw measurement records using statistical learning. By recasting higher moments of conditioned observables as supervised learning objectives, the method replaces exponentially costly sector-by-sector postselection with regression whose sample complexity is controlled by decoder capacity. In critical Ising chains, linear, logistic, and convolutional decoders recover measurement-altered scaling and correlations from simulated unpostselected data. Together, these results establish measurements as a practical and universal route to engineering, diagnosing, and exploiting new forms of quantum critical behavior.
Performing measurements on gapless quantum ground states can give rise to new universal phenomena, whose origins remain poorly understood even for the paradigmatic Ising critical point. Replica methods offer a natural framework to study such post-measurement ensembles, with the replica limit Q→1 describing physical Born-averaged observables. Here we show that, for the monitored critical Ising chain, the replicated post-measurement ensemble of states itself undergoes a phase transition precisely at the physically relevant replica limit Q→1, preventing standard replica treatments. We use boundary conformal field theory (BCFT) methods to explain the underlying mechanism of this transition. Our methods yield a perturbative analytic calculation of the universal O(1) constant in the Shannon entropy of the measurement record, previously known only numerically. We also apply our tools to study measurement-averaged spin correlators, providing a unified description of the universal properties of measurement outcomes and post-measurement states in the critical Ising chain.
The impact of projective measurements on a many-body quantum state is tightly linked to its underlying entanglement structure. Critical states are particularly sensitive, as long-range entanglement allows local measurements to have global consequences. This has been extensively studied in the context of critical states described by a conformal field theory (CFT), where measurements can alter critical properties in post-measurement quantities ('measurement-altered criticality') and induce long-range entanglement with universal features ('measurement-induced entanglement'). By contrast, little is known about the role of measurements on critical states with quenched disorder, which admit no CFT description. Here, we develop a theory of measurements on one-dimensional critical states governed by infinite-randomness fixed points (IRFPs), focusing on two closely related examples: the random XXZ chain and the random transverse-field Ising model. We show that the measurement-induced entanglement decays as a power-law with universal exponent (3−5)/2 in both models, and that the minimum number of measurements required to establish this entanglement obeys a universal scaling form. When only a finite density of measurements is made, we show that the critical properties of the state are remarkably robust: `measurement-altered criticality' is absent, with measurements either preserving the critical exponents, or destroying the criticality entirely. These results establish IRFPs as an analytically tractable arena for measurements on critical states, complementary to the CFT case. The outcome randomness that necessitates replica methods in clean systems becomes trivial at infinite randomness, with the universal response governed by the statistics induced by the quenched disorder.
Understanding the influence of measurements on the properties of many-body systems is a fundamental problem in quantum mechanics and for quantum technologies. This paper explores how a finite density of stochastic local measurement modifies a given state’s entanglement structure. Considering various measurement protocols, we explore the typical quantum correlations of their associated projected ensembles arising from the ground state of the quantum Ising model. Using large-scale numerical simulations, we demonstrate substantial differences among inequivalent measurement protocols. Surprisingly, we observe that forced on-site measurements can enhance both bipartite and multipartite entanglement. We present a phenomenological toy model and perturbative calculations to analytically support these results. Furthermore, we extend these considerations to the non-Hermitian Ising model, naturally arising in optically monitored systems, and we show that its qualitative entanglement features are not altered by a finite density of projective measurements. Overall, these results reveal a complex phenomenology where local quantum measurements do not simply disentangle degrees of freedom, but may actually strengthen the entanglement in the system.
Local measurements can alter long-range correlations in gapless quantum matter. We propose a theory of weakly-monitored Tomonaga-Luttinger liquids, a broad class of quantum critical states in one dimension. In order to address the intrinsic randomness of the measurement record, we develop a replica instanton calculation to study Born-averaged observables. We find that when measurements are relevant, average correlators of density and phase fluctuations decay at long distances as universal power laws with logarithmic corrections, a feature we argue is peculiar to measurement-induced randomness. We characterize the full multifractal spectrum of moments of correlations functions, revealing broad, strongly non-gaussian fluctuations across the ensemble of post-measurement states. We support these analytic results with matrix-product-state calculations, and provide a general picture of measurement-altered criticality for ground states described by 1+1d conformal field theories. Our results establish that physical measurements alter critical quantum states in a manner that lies beyond both forced measurements and conventional critical scaling.