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.
