We construct approximately local observables, or "overlapping qubits", using non-isometric maps and show that processes in local effective theories can be spoofed with a quantum system with fewer degrees of freedom, similar to our expectation in holography. Furthermore, the spoofed system naturally deviates from an actual local theory in ways that can be identified with features in quantum gravity. For a concrete example, we construct two MERA toy models of de Sitter space-time and explain how the exponential expansion in global de Sitter can be spoofed with many fewer quantum degrees of freedom and that local physics may be approximately preserved for an exceedingly long time before breaking down. We highlight how approximate overlapping qubits are conceptually connected to Hilbert space dimension verification, degree-of-freedom counting in black holes and holography, and approximate locality in quantum gravity.
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
−σ2lnσ2 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.
The complete evaporation of black holes, as a natural endpoint of Hawking radiation, gives rise to the black hole information paradox, which fundamentally challenges the principles of unitarity and information conservation in quantum mechanics. Although the AdS/CFT correspondence indicates that information is preserved during black hole evaporation, the precise mechanism by which it is recovered from the Hawking radiation remains an open question. To explore a potential resolution, we investigate information transfer in a spin-chain model featuring an effective horizon realized via position-dependent couplings within an XY spin chain. We derive and demonstrate Page curve-like behavior, and analyze the transmission of quantum resources, such as entanglement and coherence, across the effective horizon. Our results show that quantum resources initially localized within an interior subsystem can be transferred to the exterior via particle radiation through the horizon. This study provides a novel perspective from quantum simulation on how information may escape from black holes, thereby contributing to the further understanding of the black hole information paradox.
We present a minimal, fully unitary toy model of black hole evaporation in which information recovery emerges from non-factorized global states and observer-dependent access. The model reproduces a Page-like entropy curve for Hawking radiation without invoking fundamental information loss, horizon microstructure, or spacetime geometry at the microscopic level. The result supports the interpretation that the black hole information paradox arises from regime-dependent coarse-graining rather than from a breakdown of quantum unitarity.