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This study introduces a four-qubit quantum circuit model to simulate black hole evaporation with tunable violations of semi-causality, offering a minimal framework to analyze information leakage and residual entropy. By introducing a controlled-unitary gate, the researchers demonstrate how specific deviations from standard causality alter purification dynamics, bridging concepts from quantum gravity with tractable quantum computing architectures. The findings provide concrete insights into the interplay between unitarity preservation and horizon boundary conditions in small-scale quantum systems.
A Quantum Circuit Model of Black Hole Evaporation with Tunable Semi-Causality Violation
arXiv:2511.14350v2 Announce Type: replace-cross 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 $\mathrm{CU}(\sigma)$ 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 $\sigma=0$, the model reproduces Broda's Page-like entropy evolution with complete late-time purification. For any $\sigma>0$, 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-$\sigma$ regime, the residual entropy exhibits a characteristic $-\sigma^{2}\ln\sigma^{2}$ scaling that bears qualitative similarity to logarithmic entropy corrections in generalized uncertainty principle inspired evaporation scenarios. For larger values of $\sigma$, 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.
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 $\mathrm{CU}(\sigma)$ 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 $\sigma=0$, the model reproduces Broda's Page-like entropy evolution with complete late-time purification. For any $\sigma>0$, 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-$\sigma$ regime, the residual entropy exhibits a characteristic $-\sigma^{2}\ln\sigma^{2}$ scaling that bears qualitative similarity to logarithmic entropy corrections in generalized uncertainty principle inspired evaporation scenarios. For larger values of $\sigma$, 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.
arXiv:2511.14350 [hep-th]
(or arXiv:2511.14350v2 [hep-th] for this version)
https://doi.org/10.48550/arXiv.2511.14350 Focus to learn more arXiv-issued DOI via DataCite
Class. Quantum Grav. 43 (2026) 175011
https://doi.org/10.1088/1361-6382/ae9de6 Focus to learn more DOI(s) linking to related resources
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