ICTS

Recently, a new interpretation of gravitational spacetime in terms of quantum entanglement has been developed. The idea of holography in string theory provides a simple geometric computation of entanglement entropy. This generalizes the well-known Bekenstein-Hawking formula of black hole entropy and strongly suggests that a gravitational spacetime consists of many qubits with quantum entanglement. Also a new progress on black hole information problem has been made recently by applying this idea. A new insight on holography for de Sitter spaces have also been obtained from quantum information viewpoints. I will explain these developments in this lecture.

AdS/CFT correspondence has played crucial roles to understand difficult problems in quantum gravity in terms of quantum field theories.  When a conformal field theory (CFT) is defined on a manifold with boundaries, we can generalize the standard AdS/CFT by introducing so called end-of-the-world branes. This extended holographic duality, called AdS/BCFT, captures, for examples, the essential feature of quantum gravity such as the black hole information problem. In this lecture, I would like to explain how this holographic duality works and discuss recent developments.

Traditionally, measurements have been synonymous with extracting information from physical systems. Yet, in quantum systems measurement can actively modify and steer quantum states, acting as a quantum chisel to sculpt new patterns of entanglement. I will describe how this power of measurements can be leveraged to efficiently create the long sought after non-Abelian topological phases. Surprisingly, the particular non-Abelian states created in this way are closely related to Galois' characterization of solvable polynomial equations.
Finally, I will describe our recent collaboration with Quantinuum that utilizes this approach. In particular, I will discuss the Borromean braiding of excitations, a signature unique to non Abelian topological order, and its measurement on the Quantinuum platform.

We will see that Shannon entropy arises naturally from the problem of efficiently representing the outcome of a probabilistic experiment as a string of bits. We will review entropic quantities such as relative entropy, conditional entropy and mutual information, and relate them to notions such as the rate of growth of the number of typical sequences and asymptotic limits on the rate of information transmission across a noisy channel.

I will give an overview of notions of entanglement of color degrees of freedom relevant to the holographic correspondence

In this talk I will discuss multi-partite entanglement measures and their computation for holographic theories. I will focus on a particular class of the measures called symmetric measures. If the replica symmetry of the measure is preserved by the bulk solution, then the measure is described by a space with conical singularities whose underlying topology is that of a ball. I will show how such considerations give rise to family multi-partite measures that agree on the holographic state, answering why the holographic states are special.

The entanglement negativity is a useful measure of quantum entanglement in bipartite mixed states. The holographic dual of this entanglement measure has been controversial with calculations based on CFT techniques conflicting with calculations in random tensor networks (RTNs) that predict replica symmetry breaking. In this talk, I will argue that replica symmetry is broken for general holographic states. The argument involves relating the entanglement negativity to the 1/2 Renyi entropy of a doubled state. In order to compute it holographically, I will also discuss a modified cosmic brane proposal for computing Renyi entropies for n<1. I will comment on the differences with previous CFT calculations as well as those arising from RTNs with non-maximally entangled links.

Information-theoretic quantities such as Renyi entropies show a remarkable universality in their late-time behaviour across a variety of chaotic quantum many-body systems. Understanding how such common features emerge from very different microscopic dynamics remains an important challenge. In this talk, I will address this question in a class of Brownian models with random time-dependent Hamiltonians and a variety of different microscopic couplings. In any such model, the Lorentzian time-evolution of the n-th Renyi entropy can be mapped to evolution by a Euclidean Hamiltonian on 2n copies of the system. I will provide evidence that in systems with no symmetries, the low-energy excitations of the Euclidean Hamiltonian are universally given by a gapped quasiparticle-like band. These excitations give rise to the membrane picture of entanglement growth, with the membrane tension determined by their dispersion relation. I will establish this structure in a variety of cases using analytical perturbative methods and numerical variational techniques. I will also discuss qualitative differences in the behaviour of the second and third Renyi entropies. Overall, this structure provides an understanding of entanglement dynamics in terms of a universal set of gapped low-lying modes, which may also apply to systems with time-independent Hamiltonians.

We obtain the reflected entropy for bipartite mixed state configurations involving two disjoint and adjacent subsystems in a two dimensional boundary conformal field theory (BCFT2) in a black hole background. The bulk dual is described by an AdS3 black string geometry truncated by a Karch-Randall brane. The entanglement wedge cross section computed for this geometry matches with the reflected entropy obtained for the BCFT2 verifying the holographic duality. In this context, we also obtain the analogues of the Page curves for the reflected entropy and investigate the behaviour of the Markov gap.

We will introduce (standard) future operator algebras. We show that standard future algebras transform covariantly under the action of an emergent (universal cover of) PSL(2,R). In the case of generalized free fields with spectral densities corresponding to AdS_2 and higher dimensional eternal black holes, this symmetry corresponds to, respectively, the bulk AdS_2 and the conformal symmetry on the horizon.

In recent years, it has been realized that algebraic techniques can be used to compute formal entropy differences for semiclassical black holes in quantum gravity, and that these entropy differences are consistent with the Bekenstein-Hawking formula. I will explain how to remove the word "formal" from the previous sentence, by showing that the algebraic entropy differences have an interpretation in terms of microstate counting that is consistent with our usual ideas about statistical mechanics. Based on 2404.16098 with Akers.

Humanity faces real and present problems. Our resources to address these problems are limited. It’s easy to think, then, that we should devote ourselves to our most promising solutions.

It’s easy, but it’s wrong.

The great paradox of scientific research is that pure exploration – research into deep questions motivated by pure curiosity, without concern for applications – is ultimately what transforms our lives in tangible, practical ways.

In this talk, I will speak not just as a physicist interested in puzzles of quantum entanglement and five-dimensional black holes, but as the director of an institute devoted to fundamental research. I make the case for blue-sky research, and for optimism about our shared future.

Recently, S. Murthy has proposed a convergent expansion of free partition functions and superconformal indices of finite-N purely adjoint gauge theories based on a Fredholm determinant expansion. This expansion has been dubbed the giant graviton expansion and takes the form of an infinite series of corrections to the N=∞ result, with the m-th correction being of order exp(−mN). We show that this expansion can be reproduced using eigenvalue instantons in unitary matrix integrals. This perspective allows us to get the giant graviton expansion without the intermediate step of the Hubbard Stratonovich transformation.

Analytic continuations of areas of Ryu-Takayanagi surfaces in which the boundary subregion becomes extended along a timelike direction brought a promise of a novel, time-centric probe of the emergence of spacetime. We propose that the bulk carrier of this holographic timelike entanglement entropy are boundary-anchored extremal surfaces probing analytic continuation of holographic spacetimes into complex coordinates. This not only provides a geometric interpretation of all the known cases obtained by direct analytic continuation of closed form expressions of holographic entanglement entropy of a strip subregion, but crucially also opens a window to study holographic timelike entanglement entropy in full generality. To better understand what the prescription for holographic timelike entanglement entropy entails we study complex extremal surfaces anchored on a timelike strip on the boundary of anti-de Sitter black hole spacetimes. Our investigation reveals the existence of multiple complex extremal surfaces in these cases. We discuss physical principles that can be utilized to single out the physical contribution.

We consider linear superpositions of single particle excitations in a scalar field theory on AdS3 and evaluate their contribution to the bulk entanglement entropy across the Ryu-Takayanagi surface. We compare the entanglement entropy of these excitations obtained using the Faulkner-Lewkowycz-Maldacena formula to the entanglement entropy of linear superposition of global descendants of a conformal primary in a large c CFT obtained using the replica trick. We show that the closed from expressions for the entanglement entropy in the small interval expansion both in gravity and the CFT precisely agree. The agreement serves as a non-trivial check of the FLM formula for the quantum corrections to holographic entropy which also involves a contribution from the back reacted minimal area. Our checks includes an example in which the state is time dependent and spatially in-homogenous as well another example involving a coherent state with a Bañados geometry as its holographic dual.

I will describe extremal surfaces in de Sitter space anchored at the future boundary I+. Since such surfaces do not return, they require extra data in the past. In entirely Lorentzian dS, this leads to future-past timelike surfaces stretching between I+/I-, with pure imaginary area (relative to spacelike surfaces in AdS). With a no-boundary type boundary condition, the top half of these joins with a spacelike part on the hemisphere giving a complex-valued area. These can be thought of as certain analytic continuations from AdS while also amounting to space-time rotations. The areas are best interpreted as pseudo-entropy or time-entanglement (entanglement-like structures with timelike separations). I will also briefly discuss multiple subregions, entropy relations, the pseudo-entanglement wedge, a heuristic Lewkowycz-Maldacena formulation, as well as aspects in toy models in quantum mechanics, involving the time evolution operator, reduced transition amplitudes, and future-past entangled states.

It was conjectured that a holographic CFT deformed by the TTbar operator is dual to a bulk with a finite radial cutoff. I will describe a sequence of deformations that appear to push the cutoff surface into the black hole interior. The finite boundary is always at a constant radial surface, which means it changes signature when in the interior. I will provide a bulk path integral whose saddles describe these bulk spacetimes with finite spacelike cutoff surfaces. These results are restricted to 3d and JT gravity. This is based on work with Shadi Ali Ahmad and Simon Lin.

We will discuss the study of quantum channel capacity of Gao-Jafferis-Wall traversable wormhole protocol using coherent information.

We consider a class of exactly solvable Hamiltonian deformations of Conformal Fields Theories (CFTs) in arbitrary dimensions. The deformed Hamiltonians involve generators which form a SU(1,1) subalgebra. The Floquet and quench dynamics can be computed exactly. The CFTs exhibit distinct heating and non-heating phases at late times characterized by exponential and oscillatory correlators as functions of time. When the dynamics starts from a homogenous state, the energy density is shown to localize spatially in the heating phase. The set-ups considered will involve step pulses of different Hamiltonians, but can be generalized to smooth drives. In low dimensions we verify our results with lattice numerics.

We construct baby universe corrected bulk black hole/ white hole orthonormal basis labeled by the geodesic length of timeslice in two sided black hole. Our construction gives manifestly well defined probability distribution for length as well as transition probability to a white hole. We compute these probability distributions perturbatively, and find that late time TFD state spreads over all BH/WH basis states, i.e. Susskind's grey hole, already at the second order in perturbation. We also comment on the inherent ambiguity in our construction of our geometric basis.

The eigenstate thermalization hypothesis (ETH) provides a sufficient condition for thermalization and equilibration from any initial states in isolated systems with a large number of degrees of freedom. One part of this statement is that for large systems, the diagonal matrix elements of typical observables in the Hamiltonian eigenstate basis, that is, the expectation values of the energy eigenstates, depend smoothly on the corresponding energy values. This statement is highly related to the fact that the variance of the energy eigenstate expectation values is small. Indeed, it is conjectured that this variance shows power-law decay with respect to the Hilbert space dimension.

On the other hand, in general relativity, it is expected that heavy objects undergo gravitational collapse. Additionally, it is known that gravitational systems with black holes exhibit maximally chaotic properties. By using the holographic principle, or specifically the AdS/CFT correspondence, these facts imply that holographic theories dual to higher-dimensional Einstein gravity will show chaotic behavior and also thermalization from high-energy states. Thus, we expect that holographic theories exhibit ETH, although there is no definitive proof for this.

In this talk, we discuss that the variance of the eigenstate expectation values of primary and descendant operators shows power-law decay with respect to the Hilbert space dimension. This fact is derived from the quantum mixing properties of holographic theories with black hole gravitational duals. We also discuss the consequences of this scaling on thermalization.

This talk is based on work in progress.