A bstract According to Harlow and Hayden [ arXiv:1301.4504 ] the task of distilling information out of Hawking radiation appears to be computationally hard despite the fact that the quantum state of the black hole and its radiation is relatively un-complex. We trace this computational difficulty to a geometric obstruction in the Einstein-Rosen bridge connecting the black hole and its radiation. Inspired by tensor network models, we conjecture a precise formula relating the computational hardness of distilling information to geometric properties of the wormhole — specifically to the exponential of the difference in generalized entropies between the two non-minimal quantum extremal surfaces that constitute the obstruction. Due to its shape, we call this obstruction the ‘Python’s Lunch’, in analogy to the reptile’s postprandial bulge.
A bstract According to Harlow and Hayden [ arXiv:1301.4504 ] the task of distilling information out of Hawking radiation appears to be computationally hard despite the fact that the quantum state of the black hole and its radiation is relatively un-complex. We trace this computational difficulty to a geometric obstruction in the Einstein-Rosen bridge connecting the black hole and its radiation. Inspired by tensor network models, we conjecture a precise formula relating the computational hardness of distilling information to geometric properties of the wormhole — specifically to the exponential of the difference in generalized entropies between the two non-minimal quantum extremal surfaces that constitute the obstruction. Due to its shape, we call this obstruction the ‘Python’s Lunch’, in analogy to the reptile’s postprandial bulge.
We study the complexity of Hawking radiation for an evaporating black hole from the perspective of the stabilizer theory of quantum computation. Specifically, we calculate Wigner negativity—a magic monotone that can be interpreted as a measure of the stabilizer complexity, or equivalently, the complexity of classical simulation—in various toy models for evaporating black holes. We first calculate the Wigner negativity of Hawking radiation in the Penington-Shenker-Stanford-Yang (PSSY) model directly using the gravitational path integral, and show that the negativity is O ( 1 ) before the Page transition, but becomes exponentially large past the Page transition. We also derive a universal, information theoretic formula for the negativity that interpolates between the two extremes. We then study the Wigner negativity of radiation in a dynamical model of black hole evaporation. In this case, the negativity shows a sharp spike at early times resulting from the coupling between the black hole and the radiation system, but at late times when the system settles down, we find that the negativity satisfies the same universal formula as in the PSSY model. Finally, we also propose a geometric formula for Wigner negativity in general holographic states using intuition from fixed area states and random tensor networks, and argue that a python’s lunch in the entanglement wedge implies a stabilizer complexity that is exponentially large in 1 8 G N times the difference between the areas corresponding to the outermost and minimal extremal surfaces.
A bstract The Python’s Lunch conjecture for the complexity of bulk reconstruction involves two types of nonminimal quantum extremal surfaces (QESs): bulges and throats, which differ by their local properties. The conjecture relies on the connection between bulk spatial geometry and quantum codes: a constricting geometry from bulge to throat encodes the bulk state nonisometrically, and so requires an exponentially complex Grover search to decode. However, thus far, the Python’s Lunch conjecture is only defined for spacetimes where all QESs are spacelike-separated from one another. Here we explicitly construct (time-reflection symmetric) spacetimes featuring both timelike-separated bulges and timelike-separated throats. Interestingly, all our examples also feature a third type of QES, locally resembling a de Sitter bifurcation surface, which we name a bounce. By analyzing the Hessian of generalized entropy at a QES, we argue that this classification into throats, bulges and bounces is exhaustive. We then propose an updated Python’s Lunch conjecture that can accommodate general timelike-separated QESs and bounces. Notably, our proposal suggests that the gravitational analogue of a tensor network is not necessarily the time-reflection symmetric slice, even when one exists.
In the AdS/CFT correspondence, a subregion of the CFT allows for the recovery of a corresponding subregion of the bulk known as its entanglement wedge. In some cases, an entanglement wedge contains a locally but not globally minimal surface homologous to the CFT subregion, in which case it is said to contain a python’s lunch. It has been proposed that python’s lunch geometries should be modelled by tensor networks that feature projective operations where the wedge narrows. This model leads to the python’s lunch (PL) conjecture, which asserts that reconstructing information from past the locally minimal surface is computationally difficult. In this work, we use cryptographic tools related to a primitive known as the Conditional Disclosure of Secrets (CDS) to develop consequences of the projective tensor network model that can be checked directly in AdS/CFT. We argue from the tensor network picture that the mutual information between appropriate CFT subregions is lower bounded linearly by an area difference associated with the geometry of the lunch. Recalling that the mutual information is also computed by bulk extremal surfaces, this gives a checkable geometrical consequence of the tensor network model. We prove weakened versions of this geometrical statement in asymptotically AdS _{2+1} 2 + 1 spacetimes satisfying the null energy condition, and confirm it in some example geometries, supporting the tensor network model and by proxy the PL conjecture.
A bstract A defining property of Hawking radiation is that states with very low entanglement masquerade as highly mixed states; this property is captured by a quantum computational phenomenon known as spoofing entanglement. Motivated by the potential implications for black hole information and the emergence of spacetime connectivity, as well as possible applications of spoofing entanglement, we investigate the geometrization of two types of entanglement spoofers in AdS/CFT: so-called EFI pairs and pseudoentangled state ensembles. We show that (a strengthened version of) EFI pairs with a semiclassical bulk dual have a Python’s Lunch; the maximally mixed state over the pseudoentangled state ensemble likewise features a Python’s Lunch. Since a Python’s Lunch must lie behind an event horizon, we find that black holes are the exclusive gravitational source of entanglement spoofing in the semiclassical limit. Finally, we use an extant construction of holographic pseudorandom states to yield a candidate example of a pseudoentangled state ensemble with a semiclassical bulk dual.
This paper develops an interpretive reading of the black hole information problem within a consistency-history framework that distinguishes preservation, commitment, recoverability, feasible auditability, and public finality. Its central claim is narrow: the Page time should be understood as a transition in recoverability, not as the onset of redundant public facthood. In controlled island and quantum-extremal-surface models, an interior region associated with the black hole becomes reconstructible from the Hawking radiation after the Page transition. The paper redescribes this as a transition from hidden encoding to recoverable encoding. It does not derive the Page curve, the island formula, replica wormholes, or a solution to the black hole information problem; those results are supplied by the cited quantum-information and quantum-gravity literature. The paper argues that Hawking radiation is not, by itself, a Quantum-Darwinist broadcasting environment for the infalling microstate information. Recovery requires a large radiation region and a holistic decoding, while no small set of disjoint fragments independently carries the same infalling record. Recoverability-in-principle therefore remains distinct from strong public finality, which would require redundant, non-disturbing, and repeatable access by multiple independent observers. The Harlow–Hayden complexity barrier further separates formal reconstructibility from feasible auditability. On this reading, the Page curve schedules delayed recoverability rather than strong public finality. If the recovered information later becomes redundantly recorded in ordinary detectors and environments, that later public finality is a downstream process rather than something supplied by the black hole itself. The paper is interpretive and conceptual, has L2 status within the framework’s claim discipline, and makes no independent empirical prediction.
Abstract We argue that novel (highly nonclassical) quantum extremal surfaces (QESs) play a crucial role in reconstructing the black hole interior even for isolated, single-sided, non-evaporating black holes (i.e. with no auxiliary reservoir). Specifically, any code subspace where interior outgoing modes can be excited will have a QES in its maximally mixed state. We argue that as a result, reconstruction of interior outgoing modes is always exponentially complex. Our construction provides evidence in favor of a strong python’s lunch proposal: that nonminimal QESs are the exclusive source of exponential complexity in the holographic dictionary. We also comment on the relevance of these QESs to the geometrization of state dependence in the typicality arguments for firewalls.