# Python's lunch The recent terminology *Python's lunch* is borrowed from *The Little Prince*, where a drawing that looks like a hat to most adults is actually that of an elephant swallowed by a snake. In holography, Python's lunch refers to a bulge in the bulk spacetime geometry. ![[0196_lunch.png|400]] The Python's Lunch conjecture states that, when there are multiple extrema of the generlised entropy functional, the restricted [[0204 Quantum complexity|complexity]], $C$, of decoding an operator that lies outside the outer-minimal QES, $\gamma_{\text{desert}}$, but not outside any outer-minimal QES $\gamma_j$ for $j>0$ is given, up to an $O(1)$ correction, by $\log C=\max _{j>i:}\left[\frac{1}{2}\left(S_{\mathrm{gen}}\left(\gamma_i\right)-S_{\mathrm{gen}}\left(\gamma_j\right)\right)\right]\equiv\frac{1}{2}\left(S_{\mathrm{gen}}\left(\gamma_{\mathrm{main}}\right)-S_{\mathrm{gen}}\left(\gamma_{\mathrm{aptz}}\right)\right),$where the label $i$ and $j$ increases from the boundary to the bulk. The motivation and intuition of the conjecture comes from [[0054 Tensor network|tensor network]] models of [[0001 AdS-CFT|AdS/CFT]]. There, the presence of a bulge in the tensor network would require the presence of [[0576 Non-isometric codes|non-isometric]] operators and post selections. ## Refined proposal More generally, there are three types of QESs: - *throat*: locally minimal in space but maximal in time; - *bulge*: locally maximal in both space and time; - *bounce*: locally maximal in space but minimal in time. The refined, or general, Python's Lunch conjecture states that, to decode a bulk operator at $p$, the restricted complexity is given by$\log C=\min _{\gamma_0} \max _{\gamma_1}\left[S_{\text {gen }}\left(\operatorname{maximinimax}\left(\gamma_0, \gamma_1\right)\right)-S_{\text {gen }}\left(\gamma_1\right)\right],$where the minimisation is over QESs $\gamma_0$ such that $p$ belongs to its entanglement wedge, and the maximisation is over QESs $\gamma_1$ that belong to the entanglement wedge of $\gamma_0$. ## Refs - original proposal - [[2019#Brown, Gharibyan, Penington, Susskind]] - construction - [[2020#Bao, Chatwin-Davies, Remmen]] - converse - [[2021#Engelhardt, Penington, Shahbazi-Moghaddam (Feb)]] - strong - [[2021#Engelhardt, Penington, Shahbazi-Moghaddam (May)]] - more generally (covariant and Lorentzian) - [[2023#Engelhardt, Penington, Shahbazi-Moghaddam]] ## Related - [[0204 Quantum complexity]]