Quantum Gravity

A key question in holography is how to reconstruct bulk operators in the holographic dual. It is especially interesting to reconstruct operators inside the black hole interior, but also especially difficult to do explicitly. Recently, an explicit form for the bulk-to-boundary `holographic’ map was proposed in JT gravity, by Iliesiu, Levine, Lin, Maxfield, and Mezei, who also proposed and studied an explicit `reconstruction’ map on operators. In this talk, I will discuss various pros and cons of their reconstruction map, and propose an alternative map with perhaps nicer properties.

I will use algebras to revisit and generalize the theory of canonical purifications, explain the general concept of "CRT sewing without gravity," and explain how this technology allows the influential-but-complicated "Araki-Yamagami theorem" from the '80s to be proved with 10x less work using a QI-motivated trick. Based on work with Caminiti and Capeccia.

In holography, when two boundary subsystems have large mutual information, they are connected by their entanglement wedge. However, it remains mysterious whether these subsystems are EPR-like entangled. In this talk, I resolve this problem by finding bulk duals of one-shot distillable entanglement. Namely, I show that in one-shot scenarios: i) there is no distillable entanglement only by local operations at leading order in $G_N$, suggesting the absence of bipartite entanglement in a holographic mixed state, and ii) one-way LOCC-distillable entanglement is related to the entanglement wedge cross section, which is further dual to entanglement of formation. By demonstrating an explicit distillation protocol by holographic measurements, I conclude that a connected wedge does not necessarily imply finite distillable entanglement even when one-way LOCC is allowed. This talk is based on arXiv:2411.03426 [hep-th] and 2502.04437 [quant-ph].

The notion of complementarity, first introduced in the context of the information paradox, posits that the experiences of two observers who cannot communicate need not match in quantum gravity. In the context of the previous talk, I will argue that the recent proposals for explicitly taking observers into account provide a way to describe semiclassical closed universes in holography, at the expense of a resort to complementarity. I will then discuss an analogous setup in the case of an evaporating black hole, and propose a set of general principles for black hole complementarity. This talk is based on an ongoing collaboration with Netta Engelhardt and Daniel Harlow.

A number of recent arguments have suggested that baby universes in quantum gravity have a one-dimensional Hilbert space. I will provide a new argument, based on work with E. Gesteau, in favor of this conclusion. The argument makes use of a standard asymptotically AdS spacetime dual to a thermal state below the Hawking-Page transition. In particular, there is a low-energy, low-complexity causal wedge operator whose expectation value in the dual CFT is only consistent with a one-dimensional Hilbert space for baby universes.

The `quantum gravity in the lab' paradigm suggests that quantum computers might shed light on quantum gravity by simulating the CFT side of the AdS/CFT correspondence and mapping the results to the AdS side. This relies on the assumption that the duality map (the `dictionary') is efficient to compute. In this talk, I will argue that the complexity of the AdS/CFT dictionary is surprisingly subtle: there might be cases in which one can efficiently apply operators to the CFT state (a task we call 'operator reconstruction') without being able to extract basic properties of the dual bulk state such as its geometry (which we call 'geometry reconstruction'), and vice versa. In order to reason about the complexity of geometry reconstruction we construct examples of holographic pseudoentanglement: that is, pairs of ensembles of states that obey the Ryu-Takayanagi formula for different geometries but which are nevertheless computationally indistinguishable. This result should be compared with existing evidence that operator reconstruction is generically easy in AdS/CFT. A useful analogy for the difference between these two tasks is quantum fully homomorphic encryption (FHE): this encrypts quantum states in such a way that no efficient adversary can learn properties of the state, but operators can be applied efficiently to the encrypted state. I will show that quantum FHE can separate the complexity of geometry reconstruction vs operator reconstruction, which raises the question whether FHE could be a useful lens through which to view AdS/CFT.

The gravitational path integral remains one of the most elusive constructs in quantum gravity, particularly in regimes dominated by topological fluctuations. In this talk, I will present recent progress in Jackiw–Teitelboim (JT) gravity, where the sum over geometries can be made precise. We demonstrate that in a low-temperature regime where semiclassical approximations fail, the all-genus thermal partition function of JT gravity admits a resummation into an effective description on a single geometry with a nonlocal deformation. This construction gives formal and geometric realization to long-standing ideas from the 1980s on wormhole-induced nonlocality, linking them to ensemble interpretations and topological expansions. The resulting theory, defined on the disk with conical defect operators, captures the complete topological expansion through an emergent nonlocal interaction, providing a precise geometric window into strongly quantum gravitational dynamics.

A diffeomorphism-invariant definition of physical subsystems is crucial for understanding local quantum information in gravity. Recent toy models have made progress by adding observers with clocks and imposing boost invariance, thereby enabling a rigorous von Neumann algebraic definition of generalized entropy. But they depend on auxiliary degrees of freedom and leave infinitely many diffeomorphisms unaddressed. It is natural to ask what happens when one tries to surmount these limitations. I’ll show that including null translations lets us prove a version of the generalized second law beyond the semiclassical regime, with potential direct implications for black hole information. Then I’ll outline how the area degrees of freedom on a null surface define a quantum null time coordinate, and show how to use it to construct dressed operators invariant under all null diffeomorphisms (work in progress with Laurent Freidel.)

The SYK model has attracted significant interest for its maximal chaos, connections to two-dimensional holography, and relevance to strange metals. Two signatures of chaos in this model are out-of-time-ordered correlators (OTOCs) and Krylov complexity, both exhibiting early-time exponential behaviours characterized by the Lyapunov and Krylov exponents, respectively. In this talk, I explore these quantities in a class of relevant deformations of the SYK model, including flows which interpolate between two regions of near-maximal chaos and flows that lead to a nearly-integrable behaviour at low temperatures. I present both analytic and numerical results showing that the Krylov exponent consistently upper-bounds the Lyapunov exponent. Notably, while the Lyapunov exponent varies non-monotonically with temperature, the Krylov exponent remains smooth and monotonic, showing no clear signatures across chaotic transitions. This challenges the effectiveness of Krylov complexity as a diagnostic of chaos in quantum mechanical systems. I will also comment on the potential relevance of SYK flows for de Sitter holography and on connections to other recent works.

The holographic calculation of entanglement entropy implies that space coordinate in gravity may emerge from quantum entanglement. The next key question will be to understand how time coordinate may emerge from quantum information. After we review recent developments of pseudo entropy, which is a generalization of entanglement entropy, and its holographic calculation, we will point out that this quantity looks like a useful starting point to understand the emergence of time, by studying explicit examples of time-like entanglement entropy, traversable wormhole and dS/CFT. In the final short time, we would also like to briefly discuss how much the AdS/CFT is efficient as a quantum computer, where the notion of pseudo entanglement in the context of pseudo random states, plays an important role.