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Fractal structure of multipartite entanglement in monitored quantum circuits

Vaibhav Sharma*

Erich J. Mueller†

  • Smalley-Curl Institute and Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA

  • Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York 14853, USA

  • *Contact author: vaibhavsharma@rice.edu
  • †Contact author: em256@cornell.edu
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Phys. Rev. A 113, L060402 – Published 1 June, 2026

DOI: https://doi.org/10.1103/rdb3-gtwp

Abstract

We study the structure of multipartite entanglement in monitored quantum circuits exhibiting measurement-induced phase transitions (MIPTs). Using a one-dimensional Clifford circuit subject to local measurements with a probability p, we show numerically that the entanglement depth, corresponding to the size of the largest cluster of entangled qubits, scales as a power law with system size on both sides of the transition. The power law exponent is 1 in the entangling phase and continuously decreases to 0 as p→1 in the disentangling phase. In addition, we find that the spatial support of the largest cluster exhibits an approximate fractal geometry with a tunable fractal dimension controlled by the measurement rate. We argue that this structure arises from a competition between unitary-driven coagulation of entangled clusters and measurement-induced fragmentation, giving rise to a fractal steady state reminiscent of classical coagulation-fragmentation models. Away from the MIPT critical point, the fractal dimension matches the entanglement depth power law exponent. These results show that multipartite entanglement structure provides a fresh perspective on the emergent quantum correlations in monitored quantum circuits and noisy quantum dynamics.

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Outline

Information

Phys. Rev. A 113, L060402– Published 1 June, 2026
  • Received 24 November 2025
  • Revised 15 January 2026
  • Accepted 12 May 2026
Article part of CHORUS
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