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.
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.
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.
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≈2.1 larger than that of the standard MIPT and a negative effective central charge ceff≈−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.
We study post-measurement ensembles of ground states of tricritical and critical 1D quantum Ising Hamiltonians subjected, respectively, to weak energy and spin measurements without post-selection. These measurements act as relevant perturbations about the unmeasured critical ground states. Using finite-size renormalization group (RG) crossover analyses, we characterize their universal properties through the entanglement effective central charge, effective Affleck-Ludwig boundary entropy, and signatures of multifractality from moments of measurement-averaged correlation functions. In both cases, we find evidence for "measurement-dominated" or "measurement-altered" fixed points governed by the underlying Born-rule randomness. For critical Ising, we find a direct RG flow to a projective-measurement fixed point with area-law entanglement, whereas for the tricritical Ising model, we find evidence for a weak-measurement fixed point with logarithmic entanglement. These results clarify the RG-flow structure of weakly measured multicritical Ising ground states and show how intrinsic measurement-induced randomness can generate complex and rich universal long-distance scaling behavior in the post-measurement ensembles, accessible to controlled analytical RG and numerical finite-size RG crossover analyses.
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.
Chains of Rydberg atoms have emerged as a powerful platform for exploring low-dimensional quantum physics. This success originates from the precise control of lattice geometries provided by optical tweezers, which allows access to a wide range of synthetic quantum phases. Experiments on one-dimensional arrays have stimulated tremendous progress in understanding quantum phase transitions into crystalline phases. However, the finite width of tweezers introduces small variations in interatomic distances, leading to quenched disorder in the interactions. In this Letter, we numerically study how such disorder alters the nature of two critical regimes observed in experiments. First, following experimental protocols, we analyze Kibble-Zurek dynamics and find a crossover from the clean Ising transition to the infinite-randomness fixed point as system size and disorder strength increase. Second, we show that the floating phase-an incommensurate Luttinger liquid phase emerging at stronger interactions-is localized by the disorder, yet preserves short-range incommensurate correlations with the same leading wave vector. Our results clearly reveal an additional conceptual challenge in understanding critical phenomena using Rydberg-based quantum simulators.