Classical Cellular Automaton for Measurement-Only Entanglement Transitions
Abstract
We introduce a generalized classical long-range stochastic cellular automaton that exactly captures the entanglement dynamics and transitions of a measurement-only monitored quantum system. The corresponding quantum model consists of a one-dimensional qubit chain subject to competing single-site and long-range Bell measurements, with separations drawn from a power-law distribution. At every step of each trajectory, the state remains a tensor product of Bell pairs and unpaired qubits, with bipartite entanglement entropy fully encoded in a classical matching of the sites. This exact representation allows us to solve the dynamics analytically in several limits and to determine the steady-state scaling of the entanglement entropy. We find volume-law, fractal, and area-law regimes. Numerical results show that these regimes persist beyond the analytically solvable limit. Because Bell measurement outcomes change only the Bell-state labels and leave the matching unchanged, all subsystem entropies are outcome independent, avoiding the exponential cost of trajectory postselection often encountered in experimental studies of measurement-induced entanglement dynamics.
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BibTeX
@misc{holdhusen2026classical,
title = {{Classical Cellular Automaton for Measurement-Only Entanglement Transitions}},
author = {Will Holdhusen and Bailey M. McAmis and Armin Rahmani},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.28743},
eprint = {2609.28743},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.28743},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Classical Cellular Automaton for Measurement-Only Entanglement Transitions
AU - Will Holdhusen
AU - Bailey M. McAmis
AU - Armin Rahmani
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2609.28743
UR - https://arxiv.org/abs/2609.28743
AB - We introduce a generalized classical long-range stochastic cellular automaton that exactly captures the entanglement dynamics and transitions of a measurement-only monitored quantum system. The corresponding quantum model consists of a one-dimensional qubit chain subject to competing single-site and long-range Bell measurements, with separations drawn from a power-law distribution. At every step of each trajectory, the state remains a tensor product of Bell pairs and unpaired qubits, with bipartite entanglement entropy fully encoded in a classical matching of the sites. This exact representation allows us to solve the dynamics analytically in several limits and to determine the steady-state scaling of the entanglement entropy. We find volume-law, fractal, and area-law regimes. Numerical results show that these regimes persist beyond the analytically solvable limit. Because Bell measurement outcomes change only the Bell-state labels and leave the matching unchanged, all subsystem entropies are outcome independent, avoiding the exponential cost of trajectory postselection often encountered in experimental studies of measurement-induced entanglement dynamics.
ER -