On the Entanglement Entropy Distribution of a Hybrid Quantum Circuit

Quantum Physics [Submitted on 31 Mar 2026] On the Entanglement Entropy Distribution of a Hybrid Quantum Circuit Jeonghyeok Park, Hyukjoon Kwon, Hyeonseok Jeong We investigate the distribution of entanglement entropy in hybrid quantum circuits consisting of random unitary gates and local measurements applied at a finite rate. We demonstrate that higher moments of the entanglement entropy distribution, such as a ratio between the variance and the mean and skewness, capture nontrivial features of the measurement-induced dynamics that are invisible to the mean entropy alone. We demonstrate that these quantities exhibit distinct and robust behaviors across the volume-law and area-law phases, and can serve as effective diagnostics of measurement-induced entanglement transitions. We propose a phenomenological model describing the effect of measurements in the area-law regime, which, when combined with the directed polymer in a random environment description of the volume-law phase, well matches numerical simulations across the entire phase diagram. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2603.29323 [quant-ph]   (or arXiv:2603.29323v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2603.29323 Focus to learn more Submission history From: Jeonghyeok Park [view email] [v1] Tue, 31 Mar 2026 06:45:38 UTC (274 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-03 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)