Jonah Kudler-Flam

We consider the algebra of observables of perturbative quantum gravity in the exterior of a stationary black hole or the static patch of de Sitter spacetime. It was previously argued in Refs. [1–3] that the backreaction of gravitons on the spacetime perturbs the area of the horizon at second order, which gives rise to a nontrivial constraint on the algebra of physical observables in the subregion. The corresponding “dressed” algebra including fluctuations of the total horizon area admits a well-defined trace and is type II. In this paper we show that, at the same perturbative order at which the horizon area (and angular momentum) fluctuates, gravitational backreaction also perturbs the horizon area in an angle-dependent way. These fluctuations are encoded in horizon charges—i.e., “edge modes”—which are related to an infinite dimensional “boost supertranslation” symmetry of the horizon. Together, these charges impose an infinite family of nontrivial constraints on the gravitational algebra. We construct the full algebra of observables which satisfies these constraints. We argue that the resulting algebra is type II and its trace is shown to take a universal form. The entropy of any “semiclassical state” is the generalized entropy with an additional edge mode contribution as well as a state-independent constant. For any black hole spacetime, the algebra has no maximum entropy state and is type II ∞ . In de Sitter, the static patch is defined relative to the worldline of a localized “observer.” We show that a consistent quantization of the static-patch algebra requires a more realistic model of the observer, in which higher multipole moments perturb the “shape” of the cosmological horizon. We argue that a proper account of the observer’s rotational kinetic energy and (nongravitational) binding energy implies that the algebra is of type II 1 and thereby admits a maximum entropy state.

We develop a framework for extracting nonpolynomial analytic functions of density matrices in randomized measurement experiments by a method of analytical continuation. A central advantage of this approach, dubbed stabilized analytic continuation (SAC), is its robustness to statistical noise arising from finite repetitions of a quantum experiment, making it well suited to realistic quantum hardware. As a demonstration, we use SAC to estimate the von Neumann entanglement entropy of a numerically simulated quenched N\'eel state from R\'enyi entropies estimated via the randomized measurement protocol. We then apply the method to experimental R\'enyi data from a trapped-ion quantum simulator experiment, extracting subsystem von Neumann entropies at different evolution times. Finally, we briefly note that the SAC framework is readily generalizable to obtain other nonlinear diagnostics, such as the logarithmic negativity and R\'enyi relative entropies.

What can be measured by an observer in a cosmological universe? We address this question by constructing an algebra of gravitationally dressed observables accessible to a comoving observer in Friedmann-Lemaître-Robertson-Walker spacetimes that are asymptotically de Sitter in the past, describing an inflationary epoch. The key feature of this model, compared to previous work, is that it captures the time dependence of an expanding cosmology. An essential quantized degree of freedom is the zero mode of the inflaton, which leads to fluctuations in the effective cosmological constant during inflation and prevents the existence of a maximum entropy state in the semiclassical limit. Because of the inaccessibility of measurements beyond our cosmological horizon, we demonstrate that all states are mixed with well-defined von Neumann entropy (up to a state-independent constant). For semiclassical states, the von Neumann entropy corresponds to the generalized entropy of the observer’s causal diamond, a fine-grained quantity that is sensitive to the initial conditions of the Universe.

A bstract: We examine the behavior of sequences of states in the large N limit of AdS/CFT duality in cases in which the bulk duals involve baby universes or black holes. Such sequences generally fail to converge as pure states. Under suitable conditions, such as diverging coarse-grained entropy, they can converge to mixed states for the large N algebra, as in the case of black holes. For Euclidean preparations that produce baby universes, the sequences do not converge, due to wormhole contributions, and so these states cannot admit large N limits. Nevertheless, appropriate averaging over N can lead to convergence to a mixed state. The associated algebras have nontrivial commutants, which can possibly be interpreted as operators in the baby universe.

A bstract: While the supergravity limit of AdS/CFT has been extensively explored, the regime in which stringy dynamics dominate, characterized by the emergence of an infinite tower of higher-spin massive modes, is far less understood. In this work, we leverage techniques from algebraic quantum field theory to investigate the extent to which hallmark features of bulk gravity survive at finite string tension and the emergence of intrinsically stringy phenomena. Working in the g _s → 0 limit, we model excited string modes as free particles and demonstrate that the resulting Hagedorn spectrum leads to the breakdown of the split property, a strengthening of the locality principle, for regions that are within a string length of each other. We propose that this leads to a precise algebraic definition of stretched horizons and stretched quantum extremal surfaces. When stretched horizons exist, there is an associated nontrivial horizon ⋆-algebra. Furthermore, we investigate the algebraic ER=EPR proposal, describing the conditions for the emergence of type III von Neumann factors of all subtypes, which provides an intriguing characterization of how such regions can have a quantum Einstein-Rosen bridge even if they are geometrically disjoint.

We consider the algebra of observables of perturbative quantum gravity in the exterior of a stationary black hole or the static patch of de Sitter spacetime. It was previously argued that the backreaction of gravitons on the spacetime perturbs the area of the horizon at second-order which gives rise to a non-trivial constraint on the algebra of physical observables in the subregion. The corresponding "dressed" algebra including fluctuations of the total horizon area admits a well-defined trace and is Type II. In this paper we show that, at the same perturbative order at which the horizon area (and angular momentum) fluctuates, gravitational backreaction also perturbs the horizon area in an angle-dependent way. These fluctuations are encoded in horizon charges -- i.e., "edge modes" -- which are related to an infinite dimensional "boost supertranslation" symmetry of the horizon. Together, these charges impose an infinite family of nontrivial constraints on the gravitational algebra. We construct the full algebra of observables which satisfies these constraints. We argue that the resulting algebra is Type II and its trace is shown to take a universal form. The entropy of any "semiclassical state" is the generalized entropy with an additional "edge mode" contribution as well as a state-independent constant. For any black hole spacetime, the algebra has no maximum entropy state and is Type II$_{\infty}$. In de Sitter, the static patch is defined relative to the worldline of a localized "observer". We show that a consistent quantization of the static-patch algebra requires a more realistic model of the observer, in which higher multipole moments perturb the "shape" of the cosmological horizon. We argue that a proper account of the observer's rotational kinetic energy and (non-gravitational) binding energy implies that the algebra is of Type II$_{1}$ and thereby admits a maximum entropy state.

A bstract: We investigate the no-boundary proposal for closed universes with an observer. We argue that the observer’s no-boundary state is the identity operator on the physical Hilbert space, i.e., the maximum entropy state and show this explicitly in Jackiw-Teitelboim gravity. Geometrically, the no-boundary state is a bra-ket wormhole. Expectation values in the no-boundary state provide a trace for the observer’s algebra, which allows one to define von Neumann entropy for observers in different universes as the relative entropy with respect to the no-boundary state. This result is consistent with all previously discussed cases of traces for invariantly defined regions.

We prove an upper bound on long-range distillable entanglement in D spatial dimensions. Namely, it must decay faster than 1/r, where r is the distance between entangled regions. For states that are asymptotically rotationally invariant, the bound is strengthened to 1/r^{D}. We then find explicit examples of quantum states with decay arbitrarily close to the bound. In one dimension, we construct free fermion Hamiltonians with nearest neighbor couplings that have these states as ground states. Curiously, states in conformal field theory are far from saturation, with distillable entanglement decaying faster than any polynomial.

It is often claimed that adding a qubit to a black hole requires energy [ ] so that the extra Bekenstein–Hawking entropy can accommodate the qubit. In this essay, we explain how the recently discovered phenomenon of black hole decoherence allows quantum information to be teleported into a black hole, with arbitrarily small energy cost. The generalized second law is not violated and there is no conflict with unitarity because the teleportation creates new entanglement, analogous to Hawking radiation, between the black hole interior and exterior. In accordance with Landauer’s principle, a nonzero minimum energy cost only appears when there is a net erasure of information and noise from the exterior or, equivalently, when “zerobits” are sent into the black hole.

We consider an experimentalist, Alice, who creates a quantum superposition of a charged or massive body outside of a black hole (or, more generally, in the presence of a Killing horizon). It was previously shown that emission of soft photons/gravitons into the black hole will result in the decoherence of the components of the superposition if it is held open for a sufficiently long span of time. However, at any finite time, t c , during the process, it is not obvious how much decoherence has irrevocably occurred. Equivalently, it is not obvious how much information an observer inside the black hole can extract about Alice’s superposition prior to time t c . In this paper, we solve for the optimal experimental protocol to be followed by Alice for t > t c so as to minimize the decoherence of the components of her superposition. More precisely, given the entangling radiation that has passed through the horizon prior to the cross-section C corresponding to the time t = t c in Alice’s lab, we determine the “optimal purification” of this radiation beyond C such that the global quantum state of the radiation through the horizon has maximal overlap (quantum fidelity) with the Hartle-Hawking or Unruh vacuum. Due to the intricate low frequency entanglement structure of the quantum field theory vacuum state, we find this optimal purification to be nontrivial. In particular, even if Alice has already “closed” her superposition by bringing the components back together, we find that she can decrease the net decoherence of the components of her superposition somewhat by reopening it and performing further manipulations.