Abstract
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.
Highlights
Quantum dynamics involving unitary evolution interspersed with measurements [1,2,3] has provided a wealth of new phenomena being actively explored
For critical points involving both measurements and unitaries, we find that the mutual negativity appears to be remarkably “superuniversal”: in regimes where the mutual information scaling dimension changes continuously, the negativity scaling dimension is constant
II we introduce the definition of entanglement negativity, with a focus on “mutual negativity” of stabilizer states
Summary
Quantum dynamics involving unitary evolution interspersed with measurements [1,2,3] has provided a wealth of new phenomena being actively explored. There is a significant difference between the scaling of mutual negativity and mutual information, which contrasts sharply with that of holographic stabilizer tensor network models and relatedly, large d hybrid circuits. We illustrate these aspects and intuition in a measurement-only model [10,11,13,20], in which we analytically derive the scaling dimension for mutual negativity. V, we discuss possible future directions that might be taken along these lines, and mention a few questions that arise from this work
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