# Abstracts

*Note: Markus Müller's talk on Wednesday was cancelled.*

## Talks

### Alice Bernamonti (Florence University)

**Title:** Complexity with angular momentum

**Abstract:** I will discuss the influence of angular momentum on quantum complexity for CFT states holographically dual to rotating black holes. The holographic analysis will be complemented by the study of circuit complexity in a free scalar model for a thermofield double state with angular momentum.

### Eugenio Bianchi (Penn State University)

**Title**: Typical Entanglement, Thermalization, and Gravity

**Abstract**: Entanglement plays a central role in our current understanding of thermalization, of black hole evaporation, and of the quantum nature of spacetime geometry. In this talk, I will discuss recent results on typical entanglement entropy for ensembles of pure states defined as energy eigenstates of random Hamiltonians, and illustrate its relevance for the informational architecture of spacetime.

### Sylvain Carrozza (Radboud Universiteit Nijmegen)

**Title**: Gauge and gravitational edge modes as dynamical reference frames

**Abstract**: Due to the existence of non-local observables in gauge and gravitational theories, describing the dynamics of a bounded subregion in a gauge-invariant manner can be subtle. One possible resolution of this difficulty relies on a formal extension of the initial field-space by so-called edge modes. Those are dynamical fields intrinsic to the boundary that are postulated to transform in a specific way under the gauge group, with the purpose to restore invariance relative to gauge transformations that have non-trivial support on the boundary. I will outline a general construction identifying edge modes as explicit functionals of the global degrees of freedom, thus elucidating their physical interpretation. By serving as dynamical reference frames for the gauge group in the subregion of interest, they enable a systematic reduction of the global dynamics down to the subregion, relative to gauge-invariant boundary conditions that capture relational information between the subregion and its complement. On top of clarifying the operational meaning of edge modes, this construction leads to a principled derivation of their (pre)symplectic structure, and more generally, of boundary actions governing the subregion dynamics. I will start by introducing this formalism in the context of gauge theory, before discussing additional features of generally covariant theories, and focusing on vacuum general relativity as a primary example.

Based on: arXiv:2109.06184, in collaboration with Philipp Höhn; and arXiv:2205.00913, together with Stefan Eccles and Philipp Höhn.

### Venkatesa Chandrasekaran (IAS Princeton)

**Title**: Covariant phase space and gravitational subsystems

**Abstract**: Characterizing gravitational subsystems is a necessary step towards a better understanding of the generalized entropy. At the classical level, one way to make progress is by studying the covariant phase space of gravitational theories with boundaries. I will focus attention on subregions described by null boundaries, such as event horizons. Generically, null boundaries correspond to open Hamiltonian systems. In this setting, I will show how the covariant phase space formalism can be used to obtain unambiguous boundary charges, motivated both by AdS/CFT and the variational principle for gravitational subregions. I will discuss how central extensions of the resulting charge algebras arise from anomalous transformations of the boundary term in the gravitational action. This parallels the way in which the holographic Weyl anomaly appears in AdS/CFT, with the ambiguity in the normalization of the null generator acting analogously to the choice of Weyl frame. Finally, I will describe progress towards an understanding of black hole entropy through this formalism.

### Bin Chen (Peking University)

**Title**: Reflected Entropy in AdS_{3}/WCFT_{2}

**Abstract**: Reflected entropy is a newly proposed notion in quantum information. It has important implications in holography. In this talk, I would like to introduce our recent work on reflected entropy in 2D warped CFT, and its implication on AdS_{3}/WCFT_{2}.

### Giulio Chiribella (University of Hong Kong, University of Oxford)

**Title**: Quantum operations with indefinite time direction

**Abstract**: The fundamental dynamics of quantum particles is neutral with respect to the arrow of time. And yet, our experiments are not: we observe quantum systems evolving from the past to the future, but not the other way round. A fundamental question is whether it is in principle possible to conceive operations that probe quantum processes in the backward direction, from the future to the past, or in more general combinations of the forward and the backward direction. In this talk, I will introduce a general class operations that are not constrained to a definite time direction. As an explicit example, I will present construct an operation, called the quantum time-flip, that adds quantum control to the time direction of an unknown dynamics. This operation exhibits an information-theoretic advantage over all possible operations with definite time direction, even including operations with indefinite causal order.

### Marios Christodoulou (IQOQI Vienna)

**Title:** The search for a quantum gravity table-top signature

**Abstract:** The past years have seen intense interest in the possibility that a quantum gravity signal may be seen in a low energy `table-top' setting. An intense debate is currently ongoing on the conceptual relevance of such tests. In this talk we will briefly review recent developments and discuss some of the subtleties that arise.

### Ignacio Cirac (Max-Planck-Institute for Quantum Optics Garching)

**Title**: Quantum Circuits, Cellular Automata and Tensor Networks

**Abstract**: Quantum computers employ quantum circuits to implement algorithms. They are composed of quantum gates that act on near neighbors according to some spatial geometry. They are particular instances of quantum cellular automata (QCA), the set of operators whose action respects both locality and causality. I will show that QCAs can be effectively represented in terms of tensor networks in any spatial dimension. As a result, they obey an area law for the entanglement entropy they can create. Then, I will generalize these notions in two different ways: (i) by replacing unitary operators by quantum channels, i.e., operations that do not preserve the purity of states; (ii) by including local measurements assisted by classical communication. In the first case, the resulting operations still comply with an area law for the mutual information they can create but, in general, cannot be efficiently expressed as tensor networks. In the second, they can still give rise to unitary dynamics but cannot be described in terms of QCA in general. Joint work with Lorenzo Piroli and Goegios Styliaris

### Bianca Dittrich (Perimeter Institute)

**Title**: Areas as fundamental variables for gravity

**Abstract**: The basic variable of general relativity is the length metric. A number of results point however towards areas instead of lengths as more basic variables in quantum gravity. This includes approaches in which geometry is reconstructed from entanglement and also connection based approaches, e.g. loop quantum gravity, where areas arise as conjugate quantities to the connection. In four space-time dimensions the area metric has however far more degrees of freedom than the length metric, whereas a sharp restriction of the area metric degrees of freedom to the length metric is forbidden in the quantum theory. This leads to the long-standing question of how an area-based theory can lead to the same two propagating graviton degrees of freedom as in general relativity. I will present a resolution to this question in a discrete approach as well as in a continuum approach. I will show how an area-based formulation does lead to the two propagating graviton degrees of freedom, but also leads to (quantum) corrections. The latter can lead to signatures that may allow to distinguish length and area based approaches to gravity.

### Stefan Eccles (Okinawa Institute of Science and Technology)

**Title**: Edge modes as reference frames: subregion actions and extended symplectic structures

**Abstract**: Bounded subregions in gravitational theories have received much attention and many alternative treatments, with a hallmark feature being the appearance of edge modes. I will describe an understanding of edge modes as dynamical reference frames which relate a subregion to its complement. A systematic reduction from a global theory to a subsystem (following a post-selection procedure outlined in arXiv:2109.06184) results in consistent actions for the subregion theory, and extended symplectic structures that are closely related to other recent proposals, but exhibiting some unique features. I will summarize some of the alternatives and highlight the differences. [Based on arXiv:2205.00913, see related talk by Sylvain Carrozza.]

### Lucas Hackl (University of Melbourne)

**Title**: Quantum Information Probes: Eigenstate entanglement, entanglement of purification and reflected entropy

**Abstract**: In this talk, I will discuss some recent progress on utilizing quantum information quantities as probes to study properties of physical systems. Eigenstate entanglement refers to averaging the bipartite entanglement entropy over all eigenstates of a given Hamiltonian. I will explain how this quantity can be used as diagnostics for quantum chaos and integrability by comparing it to the averages of certain characteristic ensembles of states (such as the famous "Page curve"). Other quantities include entanglement of purification and reflected entropy, which quantify the amount of quantum correlations between two separated regions A and B in spacetime. For general conformal field theories, I will show that for large separation both quantities behave similar to the mutual information, but enhanced by an additional logarithmic correction. [based on arXiv:2112.06959 and arXiv:2102.00013/PhysRevLett.127.141604]

### Masahiro Hotta (Tohoku University)

**Title**: Expanding Edges of Quantum Hall Systems in a Cosmology Language - Hawking Radiation from de Sitter Horizon in Edge Modes

**Abstract**: Expanding edge experiments are promising to open new physics windows of quantum Hall systems. In a static edge, the edge excitation, which is described by free elds decoupled with the bulk dynamics, is gapless, and the dynamics preserve conformal symmetry. When the edge expands, such properties need not be preserved. We formulate a quantum eld theory in 1+1 dimensional curved spacetimes to analyze the edge dynamics. We propose methods to address the following questions using edge waveforms from the expanding region: Does the conformal symmetry survive? Is the nonlinear interaction of the edge excitations induced by edge expansion? Do the edge excitations interact with the bulk excitations? We additionally show that the expanding edges can be regarded as expanding universe simulators of two-dimensional dilaton-gravity models, including the Jackiw-Teitelboim gravity model. As an application, we point out that our theoretical setup might simulate emission of analog Hawking radiation with the Gibbons-Hawking temperature from the future de Sitter horizon formed in the expanding edge region.

### Veronika Hubeny (UC Davis)

**Title:** The Holographic Entropy Cone from Marginal Independence

**Abstract:** This talk will explain the recent results in characterizing the entanglement structure of geometric states in a holographic CFT, via the so-called holographic entropy cone (HEC). The relations between subsystem entanglement entropies which delimit this cone are known explicitly for only a rather coarse subdivision of the system (specified by N spatial regions, for up to N = 5). We argue that, subject to a certain graph theoretic conjecture, the task of finding the HEC for arbitrary N can be recast in terms of a much simpler combinatorial one of marginal independence which effectively reduces to the connectivity of entanglement wedges. More specifically, the N-party HEC can be reconstructed by solving the holographic marginal independence problem (HMIP) for a finer subdivision N′ ≥ N, which technically amounts to identifying which extreme rays of this subadditivity cone are realizable holographically. Curiously, despite the fact that subadditivity is a universal property which states that total correlation cannot be negative, the non-trivial facets of the HEC constructed therefrom nevertheless cannot be recast as correlation measures. (Based on 2204.00075 and further work in progress.)

### Ted Jacobson (University of Maryland)

**Title**: Causal diamonds in 2+1 dimensional quantum gravity

**Abstract**: We develop the reduced phase space quantization of causal diamonds in pure 2+1 dimensional gravity with a negative cosmological constant. The system is defined as the domain of dependence of a topological disc with fixed boundary metric. This allows quantum gravity to be studied in a novel, quasi-local context which is simple enough to be treated exactly and yet has an infinite number of degrees of freedom — the “boundary gravitons”. By solving the initial value constraints in a constant-mean-curvature time gauge and removing all the spatial gauge redundancy, we find that the phase space is the cotangent bundle of Diff^+(S^1)/PSL(2,R). To quantize this phase space we apply Isham's group-theoretic quantization scheme, with respect to a BMS_3 group, and find that the quantum theory can be realized by wavefunctions on some coadjoint orbit of the Virasoro group, taking values in a representation of the corresponding little group. We find that the twist of the diamond boundary loop is quantized in integer or half-integer multiples of the ratio of the Planck length to the boundary length. [Based on work with Rodrigo Andrade e Silva, arXiv:2203.10084]

### Achim Kempf (University of Waterloo)

**Title:** Replacing the notion of distance by the notion of correlation.

**Abstract:** The shorter the spacetime distance, the more strongly are quantum field fluctuations correlated. On this basis, the notion of spacetime distance can be replaced by the notion of correlation strength. This leads to a framework in which all fundamental degrees of freedom, be they matter degrees of freedom or be they spacetime degrees of freedom, are described by the same abstract structure: multi-point correlators. This framework is in essence information-theoretic. At low energies, these abstract correlators possess representations as n-point functions of quantum fields on a spacetime manifold and the distinction between spacetime and matter is emergent in this sense. But in the high energy quantum gravity regime, these abstract correlators may not possess representations as correlation functions of quantum fields on a spacetime manifold.

### Josh Kirklin (Okinawa Institute of Science and Technology)

**Title:** Dynamical frames in gravity: reconciling general covariance with bulk locality

**Abstract:** I will present a general formalism of dynamical gravitational reference frames that unifies the dressed and relational approaches to constructing observables. The formalism can be understood as describing a gauge-invariant form of general covariance. It allows one to define a notion of relational locality, which has many desirable properties and is arguably more physical than the usual locality associated with any fixed labelling of spacetime points. For example, it respects bulk microcausality, as I will demonstrate, in contrast to some previous approaches to bulk locality. This talk is based on joint work with Christophe Goeller and Philipp Höhn (arXiv:2206.01193).

### Isha Kotecha (Okinawa Institute of Science and Technology)

**Title:** Quantum frame relativity of subsystem dynamics and thermality

**Abstract:** Physical observations are made with respect to some reference frame. And any reference frame is fundamentally a physical system in itself, subject to quantum dynamical laws. Physical observations thus describe the system of interest relative to another system, the latter then acting as an internal quantum reference frame (QRF). In this talk, I will discuss the relativity, or not, of subsystem quantum dynamical and thermodynamical descriptions, utilising the perspective-neutral approach to quantum frame covariance. QRF relativity of tensor product structures will be seen to be crucial, especially due to the key roles played by correlations and interactions for dynamical evolution and energetics of the system. I will show how and when, the dynamical descriptions (in terms of subsystem closed/open equations of motion), and the thermodynamical descriptions (in terms of heat and work exchanges), are QRF invariant or relative. I will also present some illustrative examples encompassing the key points.

Based on upcoming work with Fabio Mele and Philipp Höhn. See related talk by Fabio Mele.

### Fabio Mele (Okinawa Institute of Science and Technology)

**Title:** On quantum frame relativity of subsystems and entanglement

**Abstract:** The absence of external relata, as it is often the case for instance in Page-Wootters dynamics, gauge theories, and quantum gravity, requires us to describe physical phenomena relative to internal subsystems. The latter play the role of internal reference frames and, as any other system, are ultimately quantum. In such a relational scenario, the partitioning of the remaining physical degrees of freedom into subsystems, their local properties, and correlations are generically contingent on the internal frame choices. In this talk, I will elaborate on such a relativity of quantum subsystems within the framework of the perspective-neutral approach to quantum reference frame (QRF) covariance. First, exploiting the fact that the physical Hilbert space does not admit any preferred tensor product structure (TPS-neutral stage), I'll explicitly show how subsystems relativity originates from the inequivalence of the physical TPSs induced by the relational observables associated with the local subalgebras in the different frame-perspectives, and provide the explicit TPS-change map. The latter allows to systematically explore the consequences for the physical description of subsystems and their properties. In particular, I'll characterise subalgebras of QRF-invariant local and non-local operators and provide conditions under which the structure of interactions and correlations will or will not change. These will be illustrated in simple examples.

Based on upcoming work with I. Kotecha and P. A. Höhn, see also related talk by I. Kotecha.

### Markus Müller (IQOQI Vienna) Talk cancelled!!!

**Title:** Quantum reference frame transformations as symmetries and the paradox of the third particle

**Abstract:** In a quantum world, reference frames are ultimately quantum systems too. This simple idea has been permeating quantum physics for decades, including quantum information theory, quantum gravity, and quantum thermodynamics. Recently, there has been a wave of interest in “internal” quantum reference frames (QRFs) that aim at describing the physical situation “from the perspective” of a given quantum subsystem. But what does this concretely mean, and how do QRF transformations differ from any other unitary map on a Hilbert space? In this talk, I describe recent work [1,2] where we show that QRF transformations appear naturally as symmetries of physical systems whose statistical properties only depend on relational data in some specific sense. We give an algebraic description of invariant and relational observables, show how the “physical Hilbert space” and other structures of constraint quantization appear naturally, and finally resolve an apparent paradox from the literature. In this “paradox of the third particle”, different QRFs seem to disagree about the consequences of discarding one of three particles, and we resolve the conflict by deriving a relational version of the partial trace. This can be viewed as a finite-dimensional analog of the problem of boundaries and edge modes in gauge theory and gravity.

[1] M. Krumm, P. A. Höhn, and M. P. Müller, Quantum 5, 530 (2021), arXiv:2011.01951.

[2] P. A. Höhn, M. Krumm, and M. P. Müller, arXiv:2107.07545.

### Rob Myers (Perimeter Institute)

**Title**: Complexity=Anything^{2}

**Abstract**: Motivated by holographic complexity, we examine a new class of gravitational observables in asymptotically AdS space associated with codimension-one slices or with codimension-zero regions. We argue that any of these observables is an equally viable candidate as the extremal volume for a gravitational dual of complexity.

### Jonathan Oppenheim (University College London)

**Title**: A post-quantum theory of classical gravity

**Abstract**: We consider two interacting systems when one is treated classically while the other remains quantum. Despite several well-known no-go arguments, consistent dynamics of this interaction exist, and we derive its most general form. Applying these results to general relativity, we present a consistent theory of classical gravity coupled to quantum field theory. The theory can be effective or fundamental, and doesn't suffer from the pathologies of the semi-classical Einstein's equation. If gravity is treated as fundamentally classical, the dynamics necessarily results in decoherence of quantum systems and a breakdown in predictability in classical phase space. Nonetheless the quantum state can remain pure conditioned on the classical trajectory and the measurement postulate of quantum theory is not needed. We prove that a trade-off between the rate of decoherence and the degree of diffusion induced in the classical system is a general feature of all classical-quantum dynamics. There is a relationship between the strength of gravitationally-induced decoherence versus diffusion of the metric. This provides an experimental test of the quantum nature of gravity. Bounds on decoherence rates arising from current interferometry experiments, combined with precision measurements of mass, already place significant restrictions on theories where a classical metric interacts with quantum matter. Based on joint work with Carlo Sparaciari, Barbara Šoda & Zachary Weller-Davies. (https://arxiv.org/abs/1811.03116, https://arxiv.org/abs/2203.01982, https://arxiv.org/abs/2203.01332)

### Daniele Oriti (Ludwig-Maximilians University)

**Title**: The universe as a quantum many-body system, cosmology as its hydrodynamics

**Abstract**: In the GFT formulation of quantum gravity, the universe is described as a quantum many-body system with basic entities being quantum simplices, glued to form extended structures by entanglement. Quantum gravity states are then generalised tensor networks, and exhibit a discrete entanglement/geometry correspondence. The emergent cosmological dynamics for the same system takes the form of condensate hydrodynamic equations on superspace, thus a non-linear extension of quantum cosmology. This prompts the exploration of general maps between the hydrodynamics of quantum fluids and cosmology, which had in fact appeared independently in the mathematical physics literature, further corroborated by the discovery of hidden symmetries in cosmological dynamics, which match those of condensate hydrodynamics. A key ingredient is the relational understanding of space and time, which makes superspace the natural arena for gravitational dynamics, as opposed to the "spacetime" manifold. These results, and the perspective they suggest, have also potential implications for analogue gravity systems in the lab.

### Alejandro Perez (CPT Marseille)

**Title**: Seeds for cosmic structure from Planckian discreteness

**Abstract**: I will present a model proposing a paradigm shift where inhomogeneities in the CMB are relics of the fundamental discreteness in the sense that they are actively produced by a quantum gravity mechanism instead of emerging from quantum fluctuations of the homogeneous vacuum state of the inflation. The model generates a (approximately) scale invariant spectrum of (adiabatic) primordial perturbations with the correct amplitudes and red tilt without an inflaton. In the construction we assume the validity of the standard model up to close to the Planck scale. The process admits a semiclassical interpretation and avoids the trans-Planckian problem of standard inflationary scenarios based on the role of vacuum fluctuations. The deviations from scale invariance observed in the CMB are controlled by the self coupling constant of the Higgs scalar. The thermal production of primordial black holes can produce the amount of cold dark matter required by observations. For natural initial conditions set at the Planck scale the amplitude and tilt of the power spectrum produced by the model fit the observations at the CMB and predict subleading corrections to the violation of scale invariance possibly measurable in the future.

### Malcolm Perry (University of Cambridge)

**Title**: The Future inside a black hole

**Abstract**: The black hole information paradox is the incompatibility of quantum mechanics with the semi-classical picture of Hawking radiation. Hawking radiation appears thermal and eventually leads to the complete disappearance of a black hole. However, black holes could be formed from a pure quantum state. The transition from such an initial state to the final state of pure Hawking radiation cannot be described by unitary time evolution. We present an analysis in quantum gravity that shows how boundary conditions in the future can prevent a loss of quantum mechanical information from the spacetime. In classical physics, the future boundary of the spacetime in the black hole interior is a singularity. Realistic gravitational collapse results in a BKL type of approach to the singularity. But, solving the Wheeler-DeWitt equation reveals that the singularity may not form and can be replaced by specifying a final state density matrix. Such a condition is natural within the context of consistent histories version of quantum mechanics.

### Sumati Surya (RRI Bengaluru)

**Title**: Spacetime Entanglement Entropy in Continuum and Discrete Spacetimes

**Abstract**: We review some recent results on Sorkin’s spacetime entanglement entropy (SSEE) for a free quantum scalar field both in the continuum and in manifold-like causal sets. In the continuum the SSEE is well defined after imposing a UV cut-off, while in the causal set, discreteness provides a natural covariant spacetime cut-off. In the continuum we calculate the SSEE for causal diamonds in a slab of 2d cylinder spacetime as well as for de Sitter and de Sitter Schwarzschild horizons. The continuum SSEE shows the expected area behaviour in all cases. On the other hand, the causal set SSEE satisfies a volume law rather than an area law for 2d and 4d de Sitter horizons. This can be traced to the characteristic non-scaling behaviour of the casual set spectrum in the deep UV. Such a volume law also appears in diverse systems like non-local field theories as well as systems with long range interactions. We speculate on what the volume law for the causal set SSEE might mean for quantum gravity.

### Tadashi Takayanagi (Kyoto University)

**Title**: CFT Dual of De Sitter Gravity in Three Dimensions

**Abstract**: In this talk, we explain the recently found holographic duality for classical gravity on a three-dimensional de Sitter space. We argue that the dual two dimensional conformal field theory (CFT) includes a special limit of SU(2) WZW CFT as its essential degrees of freedom. This reproduces perfectly partition functions in the classical gravity, including the de Sitter entropy. Moreover, we will show that studies of correlation functions and holographic entanglement entropy in this duality reveal a real time evolution in de Sitter space.

### Tomonori Ugajin (Kyoto University)

**Title**: Entanglement between two gravitating universes

**Abstract**: We study two disjoint universes in an entangled pure state. When only one universe contains gravity, the path integral for the nth Rényi entropy includes a wormhole between the n copies of the gravitating universe, leading to a standard "island formula" for entanglement entropy consistent with unitarity of quantum information. When both universes contain gravity, gravitational corrections to this configuration lead to a violation of unitarity. However, the path integral is now dominated by a novel wormhole with 2n boundaries connecting replica copies of both universes. The analytic continuation of this contribution involves a quotient by Zn replica symmetry, giving a cylinder connecting the two universes. When entanglement is large, this configuration has an effective description as a "swap wormhole", a geometry in which the boundaries of the two universes are glued together by a "swaperator". This description allows precise computation of a generalized entropy-like formula for entanglement entropy. The quantum extremal surface computing the entropy lives on the Lorentzian continuation of the cylinder/swap wormhole, which has a connected Cauchy slice stretching between the universes -- a realization of the ER=EPR idea. The new wormhole restores unitarity of quantum information.

### Aron Wall (University of Cambridge)

**Title**: Holographic Cauchy Slices

**Abstract**: I will explain how to use the T^2 deformation to reformulate the holographic principle in terms of a dual theory which lives on Cauchy slices, so that time is the emergent dimension. This new formulation interfaces with the usual AdS/CFT duality, and defines a dictionary mapping between boundary CFT states and bulk Wheeler-DeWitt states. Based on arXiv:2204.00591.