Quantum Information

One of the fundamental problems in quantum gravity is to describe the experience of a gravitating observer in generic spacetimes. In this talk, I will describe a framework within which we can analyze non-perturbative physics relative to an observer using the gravitational path integral. We apply our proposal to an observer that lives in a closed universe and one that falls behind a black hole horizon. We find that the Hilbert space that describes the experience of the observer is much larger than the Hilbert space in the absence of an observer. In the case of closed universes, the Hilbert space is not one-dimensional, as calculations in the absence of the observer suggest. Rather, its dimension scales exponentially in 1/G_N. Similarly, from an observer's perspective, the dimension of the Hilbert space in a two-sided black hole is increased and this drastically changes what an observer sees when falling past the horizon of a black hole at late times.

In this talk I will report on recent developments concerning quantization of field theories on manifolds with boundary. In perturbative AQFT this can be realized using a version of BV-BFV formalism, following the program outlined by Mnev, Cattaneo and Reshetikin. I will also argue that in pAQFT one always implicitly introduces boundaries and that there are good conceptual reasons to do so. This is joint work with Michele Schiavina.

I will describe various constructions of cosmological spacetimes with big bangs using the tools of holography. I will point out features that appear to be common to holographic models of cosmology and discuss general questions that these models might be used to understand.

The Euclidean gravitational action is unbounded below. As a result, even at the effective field theory level, the gravitational path integral cannot be formulated as an integral over real Euclidean geometries. I therefore review recent efforts to formulate the path integral directly in Lorentz-signature in a manner that allows general topology-changing transitions. I will also describe how this formulation resolves certain puzzles associated with computing the density of states for nearly-extremal black holes. (VIRTUAL TALK)

I will introduce a quantity from noncommutative probability theory called the free mutual information, and discuss how it can be used as a new diagnostic of quantum many-body chaos. This quantity captures a notion of the spreading of the operator in the abstract space of all possible time-evolved operators, rather than the more familiar notion of spreading in the physical space of degrees of freedom. I will discuss a precise relation between the free mutual information and the higher-point out-of-time-ordered correlators which applies in any system. I will further discuss the behaviour of the free mutual information in a few representative models of chaotic systems, and how it is sensitive to features of the dynamics beyond those captured by the four-point out-of-time-ordered correlator.

A scrambling unitary never destroys information according to quantum information/Shannon theory. However, this framework alone doesn’t capture the fact that scrambled information can be effectively inaccessible. This limitation points to the need for a new kind of information theory—one that quantifies how much information is scrambled, rather than how much is lost to noise. To address this, we propose introducing a new family of entropies into physics: free entropy. Unlike conventional quantum entropies, which are extensive under tensor independence, free entropy has the defining feature of extensivity under freeness—the appropriate notion of independence pertaining to quantum scrambling. I will present a preliminary result showing how free entropy naturally arises in a variant of Schumacher compression, providing it with an operational interpretation as the quantum minimum description length of quantum states. I will sketch how this interpretation extends to observables and unitaries, allowing free entropy to capture an operational aspect of quantum scrambling. Finally, I will highlight striking parallels between free entropy and von Neumann entropy, suggesting that free entropy may form the foundation of a new, complementary information theory.

I will discuss a concrete realization in N=4 SYM of the mechanism of cryptographic censorship: that sufficiently random time evolution in a holographic CFT incurs an event horizon in the bulk dual. I will show that perturbing half-BPS states by randomly distributing a large number of defects on them corresponds in the gravitational dual to exciting an extremal (horizonless) black hole to near-extremality. This random distribution of defects corresponds to acting with a typical random isometry on the half-BPS subspace. This allows us to interpret this process in the field theory as an extension of cryptographic censorship.

Our search for a quantum theory of gravity is aided by a unique and perplexing feature of the classical theory: General Relativity “knows” about its own quantum states (the entropy of a black hole), and about those of all matter (via the Quantum Focusing Conjecture). The results we are able to extract from classical gravity are inherently non-perturbative and increasingly sophisticated. Recent breakthroughs include a derivation of the entropy of Hawking radiation, a computation of the exact integer number of states of some black holes, a proof of the QFC, and the construction of gravitational holograms in general spacetimes. The nature of the oracle, and its full power, remain unknown.

The Ryu-Takayanagi formula implies that the entropy, a non-linear function of the state, is an observable in the semiclassical limit. This is a general phenomenon in a class of quantum error-correcting codes (QECC), but few specific area operators in the boundary CFT. In this work, I define a specific code in a holographic 2d CFT that includes all thermofield double states with arbitrary amounts of time evolution, but no bulk local degrees of freedom. While the naive area operator vanishes, it is possible to write down an area operator for appropriately classical states; the answer matches with previous results obtained from bulk considerations. Interestingly, this area operator involves an explicit coarse-graining. This suggests a construction for a non-isometric holographic map for these states.