Entangled Histories

We introduce quantum history states and their mathematical framework, thereby reinterpreting and extending the consistent histories approach to quantum theory. Through thought experiments, we demonstrate that our formalism allows us to analyze a quantum version of history in which we reconstruct the past by observations. In particular, we can pass from measurements to inferences about "what happened" in a way that is sensible and free of paradox. Our framework allows for a richer understanding of the temporal structure of quantum theory, and we construct history states that embody peculiar, non-classical correlations in time.Comment: 16 pages, 1 figure. v2: typo corrected, minor stylistic changes. v3: minor stylistic changes, final version for publication in Nobel Symposium NS 15

A New Relativistic Orthogonal States Quantum Key Distribution Protocol

We introduce a new relativistic orthogonal states quantum key distribution protocol which leverages the properties of both quantum mechanics and special relativity to securely encode multiple bits onto the spatio-temporal modes of a single photon. If the protocol is implemented using a single photon source, it can have a key generation rate faster than the repetition rate of the source, enabling faster secure communication than is possible with existing protocols. Further, we provide a proof that the protocol is secure and give a method of implementing the protocol using line-of-sight and fiber optic channels.Comment: 6 pages, 2 figures. To appear in QIC Vol. 14 No. 13 & 14, pp. 1081-108

AdS3_3 gravity and random CFT

We compute the path integral of three-dimensional gravity with negative cosmological constant on spaces which are topologically a torus times an interval. These are Euclidean wormholes, which smoothly interpolate between two asymptotically Euclidean AdS$_3$ regions with torus boundary. From our results we obtain the spectral correlations between BTZ black hole microstates near threshold, as well as extract the spectral form factor at fixed momentum, which has linear growth in time with small fluctuations around it. The low-energy limit of these correlations is precisely that of a double-scaled random matrix ensemble with Virasoro symmetry. Our findings suggest that if pure three-dimensional gravity has a holographic dual, then the dual is an ensemble which generalizes random matrix theory.Comment: 51+8 pages, 5 figures; v2: minor typos fixe

Renormalizing Diffusion Models

We explain how to use diffusion models to learn inverse renormalization group flows of statistical and quantum field theories. Diffusion models are a class of machine learning models which have been used to generate samples from complex distributions, such as the distribution of natural images. These models achieve sample generation by learning the inverse process to a diffusion process which adds noise to the data until the distribution of the data is pure noise. Nonperturbative renormalization group schemes in physics can naturally be written as diffusion processes in the space of fields. We combine these observations in a concrete framework for building ML-based models for studying field theories, in which the models learn the inverse process to an explicitly-specified renormalization group scheme. We detail how these models define a class of adaptive bridge (or parallel tempering) samplers for lattice field theory. Because renormalization group schemes have a physical meaning, we provide explicit prescriptions for how to compare results derived from models associated to several different renormalization group schemes of interest. We also explain how to use diffusion models in a variational method to find ground states of quantum systems. We apply some of our methods to numerically find RG flows of interacting statistical field theories. From the perspective of machine learning, our work provides an interpretation of multiscale diffusion models, and gives physically-inspired suggestions for diffusion models which should have novel properties.Comment: 69+15 pages, 8 figures; v2: figure and references added, typos correcte