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We propose entanglement negativity as a fine-grained probe of measurement-induced criticality. We motivate this proposal in stabilizer states, where for two disjoint subregions, comparing their mutual negativity and their mutual information leads to a precise distinction between bipartite and multipartite entanglement. In a measurement-only stabilizer circuit that maps exactly to two-dimensional critical percolation, we show that the mutual information and the mutual negativity are governed by boundary conformal fields of different scaling dimensions at long distances. We then consider a class of hybrid circuit models obtained by perturbing the measurement-only circuit with unitary gates of progressive levels of complexity. While other critical exponents vary appreciably for different choices of unitary gate ensembles at their respective critical points, the mutual negativity has scaling dimension 3 across remarkably many of the hybrid circuits, which is notably different from that in percolation. We contrast our results with limiting cases where a geometrical minimal-cut picture is available.
We study the entanglement behavior of a random unitary circuit punctuated by projective measurements at the measurement-driven phase transition in one spatial dimension. We numerically study the logarithmic entanglement negativity of two disjoint int
We uncover a local order parameter for measurement-induced phase transitions: the average entropy of a single reference qubit initially entangled with the system. Using this order parameter, we identify scalable probes of measurement-induced critical
We numerically investigate the structure of many-body wave functions of 1D random quantum circuits with local measurements employing the participation entropies. The leading term in system size dependence of participation entropies indicates a multif
Models for non-unitary quantum dynamics, such as quantum circuits that include projective measurements, have been shown to exhibit rich quantum critical behavior. There are many complementary perspectives on this behavior. For example, there is a kno
We study the finite-temperature superfluid transition in a modified two-dimensional (2D) XY model with power-law distributed scratch-like bond disorder. As its exponent decreases, the disorder grows stronger and the mechanism driving the superfluid t