The by-now classic Ryu-Takayanagi formula associates the entanglement entropy of a spatial region in a holographic field theory with the area of a certain minimal surface in the bulk. Despite its simplicity and beauty, this formula raises a number of stubborn conceptual problems. I will present a reformulation which does not involve the areas of surfaces. This reformulation leads to a picture of entanglement in the field theory being carried by Planck-thickness "bit threads" in the bulk.
In this talk I will consider quantum states satisfying an area law for entanglement (e.g. as found in quantum field theory or in condensed matter systems at sufficiently low temperature). I will show that both the boundary state and the entanglement spectrum admit a local description whenever there is no topological order. The proof is based on strong subadditivity of the von Neumann entropy. For topological systems, in turn, I'll show that the topological entanglement entropy quantifies exactly how many extra bits are needed in order to have a local description for the boundary state.
I will describe a procedure for reconstructing the metric of a general holographic spacetime (up to an overall conformal factor) from distinguished spatial slices - “light-cone cuts” - of the conformal boundary. This reconstruction can be applied to bulk points in causal contact with the boundary. I will also discuss a prescription for obtaining the light-cone cuts from divergences of correlators in the dual field theory.
The application of holography to fundamental problems in quantum gravity has been hindered by the lack of a solvable model. However, building on work by Sachdev and Ye, Kitaev has proposed a solvable QM system as a dual to an AdS2 black hole. I will discuss the model and its possible bulk interpretation.
the multi-scale entanglement renormalization ansatz (MERA) is a tensor network that efficiently represents the ground state wave-function of a lattice Hamiltonian. Similarly, its extension to the continuum, the continuous MERA [proposed by Haegeman, Osborne, Verschelde and Verstraete, Phys. Rev. Lett. 110, 100402 (2013), arXiv:1102.5524], aims to efficiently represent the vacuum state wave-functional of a quantum field theory.
In this talk I consider the following principle that one may impose on any physical theory T:
"If an agent uses T to describe a system which includes another agent who herself uses T then no logical contradictions should arise.”
I then propose a gedankenexperiment, which can be regarded as an extension of the Wigner’s Friend experiment, to test whether this principle holds for quantum mechanics. The conclusion is that this is indeed the case for “plain" quantum theory, but that the principle is violated by many of its common interpretations and extensions.
I enumerate the cases in 2d CFT when the modular hamiltonian (log of the reduced density matrix) may be written as an appropriate integral over the energy-momentum tensor times a local weight. This includes known examples as well as new time-dependent ones. In all these cases the entanglement spectrum is that of an appropriate boundary CFT. I point out the obstruction to the existence of such a result for more complicated bipartitions of the space. This is joint work with Erik Tonni