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 outcomes affect only Bell-state labels and not the matching, all subsystem entropies are outcome independent, avoiding the exponential cost of trajectory postselection.

Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech)

arXiv:2609.28743 [quant-ph]

(or arXiv:2609.28743v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.28743 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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