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 $(3-\sqrt{5})/2$ 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.
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.
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.
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.
We study the effects of measurements, performed with a finite density in space, on the ground state of the one-dimensional transverse-field Ising model at criticality. Local degrees of freedom in critical states exhibit long-range entanglement, and as a result, local measurements can have highly nonlocal effects. Our analytical investigation of correlations and entanglement in the ensemble of measured states is based on properties of the Ising conformal field theory (CFT), where measurements appear as (1+0)-dimensional defects in the (1+1)-dimensional Euclidean spacetime. So that we can verify our predictions using large-scale free-fermion numerics, we restrict ourselves to parity-symmetric measurements. To describe their averaged effects analytically we use a replica approach, and we show that the defect arising in the replica theory is an irrelevant perturbation to the Ising CFT. Strikingly, the asymptotic scalings of averaged correlations and entanglement entropy are therefore unchanged relative to the ground state. In contrast, the defect generated by postselecting on the most likely measurement outcomes is exactly marginal. We then find that the exponent governing postmeasurement order parameter correlations, as well as the ``effective central charge'' governing the scaling of entanglement entropy, vary continuously with the density of measurements in space. Our work establishes connections between the effects of measurements on many-body quantum states and of physical defects on low-energy equilibrium properties.
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.
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.
We consider the effects of weak measurements on the quantum critical ground state of the one-dimensional (a) tricritical and (b) critical quantum Ising model, by measuring in (a) the local energy and in (b) the local spin operator in a lattice formulation. By employing a controlled renormalization group (RG) analysis we find that each problem exhibits highly complex novel scaling behavior, arising from the intrinsically indeterministic ('random') nature of quantum mechanical measurements, which is governed by a measurement-dominated RG fixed point that we study within an ε expansion. In the tricritical Ising case (a) we find (i): multifractal scaling behavior of energy and spin correlations in the measured groundstate, corresponding to an infinite hierarchy of independent critical exponents and, equivalently, to a continuum of universal scaling exponents for each of these correlations; (ii): the presence of logarithmic factors multiplying powerlaws in correlation functions, a hallmark of 'logarithmic conformal field theories' (CFT); (iii): universal 'effective central charges' cn(eff) for the prefactors of the logarithm of subsystem size of the nth Rényi entropies, which are independent of each other for different n, in contrast to the unmeasured critical ground state, and (iv): a universal ("Affleck-Ludwig") 'effective boundary entropy' Seff which we show, quite generally, to be related to the system-size independent part of the Shannon entropy of the measurement record, computed explicitly here to 1-loop order. - A subset of these results have so-far also been obtained within the ε expansion for the measurement-dominated critical point in the critical Ising case (b).