In holography, the quantum extremal surface formula relates the entropy of a boundary state to the sum of two terms: the area term and the entropy of bulk fields inside the entanglement wedge. As the bulk effective field theory suffers from UV divergences, the second term must be regularized. It has been conjectured since the work of Susskind and Uglum that the renormalization of Newton’s...
We argue that generic local subregions in semiclassical quantum gravity are associated with von Neumann algebras of type II_1, extending recent work by Chandrasekaran et.al. beyond subregions bounded by Killing horizons. The subregion algebra arises as a crossed product of the type III_1 algebra of quantum fields in the subregion by the flow generated by a gravitational constraint operator. We...
We quantize JT gravity with matter on the spatial interval with two asymptotically AdS boundaries. We consider the von Neumann algebra generated by the right Hamiltonian and the gravitationally dressed matter operators on the right boundary. We prove that the commutant of this algebra is the analogously defined left boundary algebra and that both algebras are type II infinity factors. These...
We show that if a massive (or charged) body is put in a quantum superposition of spatially separated states in the vicinity of any (Killing) horizon, the mere presence of the horizon will eventually destroy the coherence of the superposition in a finite time. This occurs because, in effect, the long-range fields sourced by the superposition register on the black hole horizon which forces the...
We describe supersymmetric SYK models which display a scaling similarity at low temperatures, rather than the usual conformal behavior. We discuss the large N equations, which were studied previously as uncontrolled approximations to other models. We also present a picture for the physics of the model which suggest that the relevant low energy degrees of freedom are almost free. We also...
We probe the multipartite entanglement structure of the vacuum state of a CFT in 1+1 dimensions, using recovery operations that attempt to reconstruct the density matrix in some region from its reduced density matrices on smaller subregions. We use an explicit recovery channel known as the twirled Petz map, and study distance measures such as the fidelity, relative entropy, and trace distance...
In this talk, we will first present an analysis of infinitesimal null deformations for the entanglement entropy, which leads to a major simplification of the proof of the C, F and A-theorems in quantum field theory. Next, we will discuss the quantum null energy condition (QNEC) on the light-cone. Finally, we combine these tools in order to establish the irreversibility of renormalization group...
We study Generalized Free Fields (GFF) from the point of view of information measures. We begin by reviewing conformal GFF, their holographic representation, and the multiple possible assignations of algebras to a single spacetime region that arise in these theories. We will focus on manifestations of these features present in the Mutual Information (MI) of holographic GFF. First, we show that...
Motivated by the ground state structure of quantum models with all-to-all interactions such as mean-field quantum spin glass models and the Sachdev-Ye-Kitaev (SYK) model, we propose a tensor network architecture which can accomodate volume law entanglement and a large ground state degeneracy. We call this architecture the non-local renormalization ansatz (NoRA) because it can be viewed as a...
Holographic quantum-error correcting codes are models of bulk/boundary dualities such as the anti-de Sitter/conformal field theory (AdS/CFT) correspondence, where a higher-dimensional bulk geometry is associated with the code's logical degrees of freedom. Previous discrete holographic codes based on tensor networks have reproduced the general code properties expected from continuum AdS/CFT,...
We study entanglement entropy in (2+1)-dimensional gravity as a window into larger open questions regarding entanglement entropy in gravity. (2+1)-dimensional gravity can be rewritten as a topological field theory, which makes it a more tractable model to study. In these topological theories, there remain key questions which we seek to answer in this work, such as the questions 1) What is the...
In holographic CFTs satisfying eigenstate thermalization, there is a regime where the operator product expansion can be approximated by a random tensor network. The geometry of the tensor network corresponds to a spatial slice in the holographic dual, with the tensors discretizing the radial direction. In spherically symmetric states in any dimension and more general states in 2d CFT, this...
We investigate the link between position-based quantum cryptography (PBQC) and holography established in [May19] using holographic quantum error correcting codes as toy models. If the "temporal" scaling of the AdS metric is inserted by hand into the toy model via the bulk Hamiltonian interaction strength we recover a toy model with consistent causality structure. This leads to an interesting...
Within the setting of the AdS/CFT correspondence, we ask about the power of computers in the presence of gravity. We show that there are computations on $n$ qubits which cannot be implemented inside of black holes with entropy less than $O(2^n)$. To establish our claim, we argue computations happening inside the black hole must be implementable in a programmable quantum processor, so long as...
Quantum simulation of lattice gauge theory is expected to become a major application of near-term quantum devices. In this presentation, I will talk about a quantum simulation scheme for lattice gauge theories motivated by Measurement-Based Quantum Computation [1], which we call Measurement-Based Quantum Simulation (MBQS). In MBQS, we consider preparing a resource state whose entanglement...
We demonstrate that some quantum teleportation protocols exhibit measurement induced phase transitions in Sachdev-Ye-Kitaev model. Namely, Kitaev-Yoshida and Gao-Jafferis-Wall protocols have a phase transition if we apply them at a large projection rate or at a large coupling rate respectively. It is well-known that at small rates they allow teleportation to happen only within a small...
Holography has taught us that spacetime is emergent and its properties depend on the entanglement structure of the dual boundary theory. At the same time, we know that local projective measurements tend to destroy entanglement. This leads to a natural question: what happens to the holographic bulk spacetime if we perform strong local projective measurements on a subsystem $A$ of the boundary?...
We analyze the effect of decoherence, modelled by local quantum channels, on quantum critical states and we find universal properties of the resulting mixed state's entanglement, both between system and environment and within the system. Renyi entropies exhibit volume law scaling with a subleading constant governed by a "g-function" in conformal field theory (CFT), allowing us to define a...
When gravity is sourced by a quantum system, there is tension between its role as the mediator of a fundamental interaction, which is expected to acquire nonclassical features, and its role in determining the properties of spacetime, which is inherently classical. Fundamentally, this tension should result in breaking one of the fundamental principles of quantum theory or general relativity,...
We propose a conceptually new class of dynamical experiments whose goal is to falsify the hypothesis that an interaction between quantum systems is mediated by a purely local classical field. The systems we study implement a dynamics that cannot be simulated by means of local operations and classical communication (LOCC), even when no entanglement is ever generated at any point in the process....
We analyse models of Matrix Quantum Mechanics in the double scaling limit that contain non-singlet states. The finite temperature partition function of such systems contains non-trivial winding modes (vortices) and is expressed in terms of a group theoretic sum over representations. We then focus on the model of Kazakov-Kostov-Kutasov when the first winding mode is dominant. In the limit of...
We present a construction in which the origin of black hole entropy gets clarified. We start by building an infinite family of geometric microstates for black holes in general relativity. This construction naively overcounts the Bekenstein-Hawking entropy. We then describe how wormholes in the Euclidean path integral for gravity cause these states to have exponentially small, but universal,...
We consider the quantum gravity partition function that counts the dimension of the Hilbert space of a spatial region with topology of a ball and fixed proper volume, and evaluate it in the leading order saddle point approximation. The result is the exponential of the Bekenstein-Hawking entropy associated with the area of the saddle ball boundary, and is reliable within effective field theory...
The Spectral Form Factor is an important diagnostic of level repulsion Random Matrix Theory (RMT) and quantum chaos. The short-time behavior of the SFF as it approaches the RMT result acts as a diagnostic of the ergodicity of the system as it approaches the thermal state. In this work we observe that for systems without time-reversal symmetry, there is a second break from the RMT result at...
66 - It has been proposed that the exponential decay and subsequent power law saturation of out-of-time-order correlation functions can be universally described by collective 'scramblon' modes. We develop this idea from a path integral perspective in several examples, thereby establishing a general formalism. After reformulating previous work on the Schwarzian theory and identity conformal...
The Sachdev-Ye-Kitaev (SYK) model is a simple toy model of holography that has seen widespread study in the area of quantum gravity. It is particularly notable for its feasibility of simulation on near-term quantum devices. Recently, Swingle et al. introduced a sparsified version of the SYK model and analyzed its holographic properties, which are remarkably robust to deletion of Majorana...
In this paper, we explore the possibility of building a quantum memory that is robust to thermal noise using large N matrix quantum mechanics models. First, we investigate the gauged SU(N) matrix harmonic oscillator and different ways to encode quantum information in it. By calculating the mutual information between the system and a reference which purifies the encoded information, we identify...
We construct approximately local observables, or "overlapping qubits", using non-isometric maps and show that processes in local effective theories can be spoofed with a quantum system with fewer degrees of freedom, similar to our expectation in holography. Furthermore, the spoofed system naturally deviates from an actual local theory in ways that can be identified with features in quantum...
The JLMS formula is a cornerstone in our understanding of bulk reconstruction in holographic theories of quantum gravity, best interpreted as a quantum error-correcting code. Moreover, recent work has highlighted the importance of understanding holography as an approximate and perhaps non-isometric code. In this work, we construct an enlarged code subspace for the bulk theory that contains...
Recently, Akers et al. proposed a non-isometric holographic map from the interior of a black hole to its exterior. Within this model, we study properties of the black hole S-matrix, which are in principle accessible to observers who stay outside the black hole. Specifically, we investigate a scenario in which an infalling agent interacts with radiation both outside and inside the black hole....
In this talk I will present recent results about the computational complexity of determining homology groups of simplicial complexes, a fundamental task in computational topology. In arXiv:2209.11793 we showed that this decision problem is QMA1-hard. Moreover, we showed that a version of the problem satisfying a suitable promise is contained in QMA. This suggests that the seemingly classical...
