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arXiv · 2511.08690

Fractal structure of multipartite entanglement in monitored quantum circuits

Vaibhav Sharma·Erich J Mueller
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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 $p \to 1$ 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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Vaibhav Sharma, Erich J Mueller. 2025-11-11. Fractal structure of multipartite entanglement in monitored quantum circuits. https://doi.org/10.1103/rdb3-gtwp

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