Entanglement Negativity at Measurement-Induced Criticality

TL;DR

This paper introduces entanglement negativity as a detailed measure to analyze measurement-induced criticality in quantum circuits, revealing universal scaling behaviors and distinctions from percolation models.

Contribution

It proposes using entanglement negativity to distinguish bipartite and multipartite entanglement at measurement-induced critical points, and demonstrates its universal scaling in hybrid quantum circuits.

Findings

Mutual negativity and mutual information scale with boundary conformal fields.

Mutual negativity maintains a scaling dimension of 3 across various hybrid circuits.

Results differ from classical percolation models, indicating unique quantum critical behavior.

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.