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Cryptographic tests of the python's lunch conjecture

by Alex May, Sabrina Pasterski, Chris Waddell, Michelle Xu

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Submission summary

Authors (as registered SciPost users): Chris Waddell
Submission information
Preprint Link: https://arxiv.org/abs/2411.10527v4  (pdf)
Date accepted: Aug. 22, 2025
Date submitted: April 15, 2025, 8:58 p.m.
Submitted by: Chris Waddell
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
Specialties:
  • High-Energy Physics - Theory
Approach: Theoretical

Abstract

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$_{2+1}$ spacetimes satisfying the null energy condition, and confirm it in some example geometries, supporting the tensor network model and by proxy the PL conjecture.

Author indications on fulfilling journal expectations

  • Provide a novel and synergetic link between different research areas.
  • Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
  • Detail a groundbreaking theoretical/experimental/computational discovery
  • Present a breakthrough on a previously-identified and long-standing research stumbling block

Published as SciPost Phys. 19, 084 (2025)

Reports on this Submission

Report #2 by Anonymous (Referee 2) on 2025-8-2 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:2411.10527v4, delivered 2025-08-02, doi: 10.21468/SciPost.Report.11681

Report

In this article, the authors use a tool from cryptography called the "conditional disclosure of secrets" (CDS) to test the python's lunch conjecture in AdS/CFT. The python's lunch conjecture states that the reconstruction of bulk degrees of freedom in the portion of the entanglement wedge contained behind the outermost extremal surface is computationally hard. The conjecture is strongly motivated by the analogy between the bulk spacetime in AdS/CFT and tensor networks. In the present article, the authors first develop a new computationally secure CDS task (where the secret is only protected against computationally bounded referees when the condion is not met) and prove an information theoretic constraint -- a lower bound on the minimum necessary mutual information between the two parties Alice (A) and Bob (B) holding the keys, such that they are able to accomplish computationally secure CDS. Assuming the python's lunch conjecture, the authors then show that for a region with a python's lunch (to be thought of as the referee system), it is possible to construct subregions A and B which can successful carry out the computationally secure CDS task by meeting in the bulk, and hiding the secret in the python's lunch region if the condition is not met. Further, taking inspiration from tensor network ideas (the same kind that appear in the python's lunch conjecture), the authors show that in the holographic context, their lower bound on the mutual information translates to a concrete geometric statement, which they then check in the AdS3 context.

The paper is very clearly written, and the ideas presented here are novel, creative and of wide interest to the AdS/CFT community. Furthermore, their theorem proving the lower bound on mutual information for computational secure CDS might be of indepedent interest to the quantum information/computer science community. I strongly recommend publication of this article in Scipost.

Recommendation

Publish (easily meets expectations and criteria for this Journal; among top 50%)

  • validity: -
  • significance: -
  • originality: -
  • clarity: -
  • formatting: -
  • grammar: -

Report #1 by Matthew Headrick (Referee 1) on 2025-6-10 (Invited Report)

  • Cite as: Matthew Headrick, Report on arXiv:2411.10527v4, delivered 2025-06-10, doi: 10.21468/SciPost.Report.11377

Report

This paper combines two recent strains of work in holography: the “quantum tasks” framework of May and collaborators, which explores computational processes that are non-local on the boundary but local in the bulk; and the python’s lunch conjecture of Brown et al, which posits an exponential complexity cost in bulk reconstruction for regions caught between the RT (or HRT) surface and an outermost extremal surface. The combination of these two sets of ideas is achieved by defining a bulk protocol that accomplishes a cryptographic task called “conditional disclosure of quantum secrets”. As the authors show, successfully carrying out this task requires two parties (represented by boundary regions) to share a large mutual information, and therefore a connected entanglement wedge. More quantitatively, by invoking the PLC, the authors place a lower bound on the mutual information in terms of the areas of certain bulge and appetizer surfaces. They test this geometric inequality in certain 2+1 dimensional spacetimes, and prove a weakened version of it. The fact that it is possible to incorporate the PLC into a sensible conjecture about holographic CDQS can be taken as support for the former conjecture.

The explorations in this paper push against the boundary of our understanding of the role of computational complexity in holography and quantum gravity. Hopefully, in the future, the various conjectures in the paper can be proven or disproven, sharpening our understanding of this still somewhat fuzzy area.

The paper is technically correct as far as I can tell, the writing is honest and clear, and the results are novel and interesting. I recommend publication in SciPost Physics.

Requested changes

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Recommendation

Publish (easily meets expectations and criteria for this Journal; among top 50%)

  • validity: top
  • significance: high
  • originality: high
  • clarity: high
  • formatting: perfect
  • grammar: excellent

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