Online Workshop on Qubits and Black Holes
December 7-9, 2020
Chris Akers, Massachusetts Institute of Technology
Title: Quantum Minimal Surfaces from Quantum Error Correction
Abstract: What is the role of quantum extremal surfaces (QES) in general quantum error-correcting codes? I will present preliminary results starting to answer this question, expanding on the previous work of Harlow, providing necessary and sufficient conditions for a general code to satisfy a quantum minimal surface prescription.
Adam Bouland, University of California, Berkeley
Title: Pseudorandomness and the AdS/CFT Correspondence
Abstract: Could quantum circuit complexity have physical ramifications? In the context of AdS/CFT, Susskind has suggested that it might, as circuit complexity could be the CFT dual to AdS wormhole volume. Here we explore this proposal using cryptographic techniques. We first show how to create pseudorandom quantum states in the CFT, thereby arguing that their quantum circuit complexity is not "feelable", in the sense that it cannot be approximated by any efficient experiment. By contrast we argue that the wormhole volume is "feelable" in some general but non-physical sense. The duality between a "feelable" quantity and an "unfeelable" quantity implies that some aspect of this duality -- either the AdS/CFT dictionary, or else the dynamics of quantum gravity -- must have exponential complexity. While at first sight this might seem to justify the discomfort of complexity theorists with equating complexity with a physical quantity, a further examination of our arguments shows that these conclusions are an inevitable consequence of the "wormhole growth paradox" which inspired this proposal in the first place. Based largely on https://arxiv.org/abs/1910.14646
Netta Engelhardt, Massachusetts Institute of Technology
Title: Free Energy from Replica Wormholes
Abstract: I will discuss progress towards understanding the relationship between the gravitational path integral and the partition function via the gravitational free energy (more generally the generating functional). A proper computation of the free energy requires a replica trick distinct from the usual one used to compute the entropy. I will show that in JT gravity there is a regime where the free energy computed without replica wormholes is pathological. Interestingly, the naive inclusion of replica wormholes is not quite sufficient to resolve the pathology: an alternative analytic continuation is required. I will discuss the implications of this for various interpretations of the gravitational path integral (e.g. as computing an ensemble average) and also mention some parallels with spin glasses.
Lampros Lamprou, Massachusetts Institute of Technology
Title: Inside the Hologram: The Bulk Observer's Experience
Abstract: I will present a holographic framework for reconstructing the experience of bulk observers in AdS/CFT. In particular, I will show how to recover the proper time and energy distribution measured along bulk worldlines, directly in the CFT via a universal, background-independent prescription. For an observer falling into an eternal AdS black hole, the proposal resolves a conceptual puzzle raised by Marolf and Wall. It suffers, however, from the "frozen vacuum" problem for which I will offer some preliminary comments. Notably, the approach does not depend crucially on the asymptotic Hamiltonian and it outlines a general framework for the emergence of time.
Javier Magan, Instituto Balseiro, Centro Atómico de Bariloche
Title: Entropic Order Parameters for the Phases of QFT
Abstract: We start by describing how generalized symmetries in QFT arise in the violation of elementary properties that appear when we associate algebras to regions in QFT. This observation provides a new perspective/proof of the abelian nature of generalized symmetries. Further, the algebra of order/disorder parameters is fixed and can be deduced without the explicit construction of the non-local operators. In these scenarios, there are two natural algebras associated with regions of specific topologies, suggesting a simple geometrical order parameter defined as a relative entropy. These relative entropies satisfy a “certainty relation” connecting the statistics of the order and disorder parameters. We describe old and new aspects of the phases of QFT’s with generalized symmetries from this perspective. In particular, the certainty relation makes transparent the duality between constant and area law behaviors in symmetry-breaking scenarios, and in CFT’s there are relative entropies exactly computable.
Alex May, University of British Columbia
Title: Quantum Tasks in Holography
Abstract: Quantum tasks are quantum computations which have inputs and outputs that occur at designated spacetime locations. Understanding which tasks are possible to complete, and what resources are required to complete them, captures spacetime-specific aspects of quantum information. In this talk we explore how an understanding of quantum tasks can be applied to AdS/CFT. We find that tasks reveal a connection between causal features of bulk geometry and boundary entanglement. We discuss the connected wedge theorem, which makes this connection precise. In the context of AdS spacetimes with end-of-the-world branes, the connected wedge theorem suggests a causal relationship between islands and their corresponding radiation systems.
Thomas Mertens, Ghent University
Title: Liouville and JT Quantum Gravity - Holography and Matrix Models
Abstract: I will discuss recent progress in understanding quantum gravity amplitudes (partition function, boundary correlation functions and multiboundary amplitudes) in Liouville gravity, and how they limit to Jackiw-Teitelboim (JT) amplitudes. I will provide two perspectives on the results: the Liouville gravity answers look like q-deformations of the JT answers, and Liouville gravity can be related to a 2d dilaton gravity with a sinh dilaton potential. Based largely on arXiv:2006.07072 and 2007.00998.
Geoffrey Penington, University of California, Berkeley
Title: Life without Pythons would be so Simple
Abstract: Reconstruction of bulk operators within the causal wedge is simple to achieve using Lorentzian causal bulk dynamics. In contrast, the only known methods for reconstructing arbitrary operators in the full entanglement wedge (the Petz map, modular flow etc.) are highly complex from a boundary perspective. It was previously argued based on intuition from tensor networks that this complexity is necessary if the bulk operator hidden behind an extremal surface (in a ‘python’s lunch’). However in general there may be operators which are not in a lunch, but are also not in the causal wedge. I will argue that such operators can also be simply, and causally, reconstructed by gradually expanding the causal wedge using time folds with different boundary conditions.
Mukund Rangamani, University of California, Davis
Title: Real-Time Gravitational Replicas
Abstract: I will discuss real-time path integrals in gravitational theories. As applications we will describe the general structure of replica wormhole saddles and the effective dynamics of open quantum systems with long-term memory.
Monika Schleier-Smith, Stanford University
Title: Programmable Non-Local Interactions: Towards Fast Scrambling with Cold Atoms
Abstract: The quest to build and probe toy models of quantum gravity in table-top experiments presents a new frontier for the field of quantum simulation. One challenge is to simulate fast scrambling of quantum information in black holes, for which a key requirement is to engineer a quantum system with a non-local graph of interactions. I will report on advances in control of non-local interactions in experiments with cold atoms. By coupling the atoms to light in an optical resonator, we generate tunable non-local Heisenberg interactions, which we characterize by imaging the resulting phases and dynamics. Notable observations include interaction-based protection of spin coherence and photon-mediated spin-mixing, a mechanism for generating correlated atom pairs. I will present recent results on optically programming the distance-dependence of the spin-spin couplings, with prospects for studying fast scrambling and for accessing treelike (p-adic) geometries akin to hyperbolic space.
Douglas Stanford, Stanford University
Title: Comments about Wormholes and Quantum Noise
Abstract: We will comment on wormholes for the off-diagonal components of the density matrix of Hawking radiation. Then we will discuss work in progress on a simple model in which small effects associated with unitarity of time evolution may be related to further topologies.
Edward Witten, Institute for Advanced Study
Title: Some Comments on Energy Inequalities
Abstract: The talk will consist of some general observations about energy inequalities, such as the statement that the energy density averaged over a time-like curve is bounded below and the statement that the averaged null energy on a null geodesic in Minkowski space is nonnegative.