A Quantum Circuit Model of Black Hole Evaporation with Tunable Semi-Causality Violation

Abstract We present a four-qubit quantum circuit model of black-hole evaporation with a controlled violation of semi-causality, understood as the condition that information may fall into the black hole but cannot propagate back across the horizon. Building on Broda’s semi-causal evaporation circuit, we introduce a controlled-unitary gate CU ( σ ) that allows tunable information leakage from the interior to the exterior while preserving global unitarity. We compute the single-qubit reduced entropies, together with the mutual information and entanglement negativity for the BH-GR and IN–OUT bipartitions, at each discrete time step. For σ = 0 , the model reproduces Broda’s Page-like entropy evolution with complete late-time purification. For any σ > 0 , however, nonzero residual single-qubit entropies and persistent late-time entanglement remain, indicating incomplete purification of the outgoing radiation despite the global unitary evolution. In the small- σ regime, the residual entropy exhibits a characteristic − σ 2 ln ⁡ σ 2 scaling that bears qualitative similarity to logarithmic entropy corrections in generalized-uncertainty-principle inspired evaporation scenarios. For larger values of σ , the persistence of finite residual entropy invites comparison with remnant-like endpoint configurations in regular or extremal black-hole models. Our results show how controlled departures from the semi-causal limit modify information recovery in a minimal analytically tractable model of black-hole evaporation.