Final PhD Oral Examination (Thesis Title: “Aspects of Quantum Information in Quantum Field Theory and Quantum Gravity”)
Physics and Astronomy
We discuss applications of quantum information theoretic concepts to quantum gravity and the low-energy regime of quantum field theories.
The first part of this thesis is concerned with how quantum information spreads in four-dimensional scattering experiments for theories coupled to quantum electro- dynamics or perturbative quantum gravity. In these cases, every scattering process is accompanied by the emission of an infinite number of soft photons or gravi-tons, which cause infrared divergences in the calculation of scattering probabilities.
There are two methods to deal with IR divergences: the inclusive and dressed formalisms. We demonstrate that in the late-time limit, independent of the method, the hard outgoing particles are entangled with soft particles in such a way that the reduced density matrix of the hard particles is essentially completely decohered.
Furthermore, we show that the inclusive formalism is ill-suited to describe scattering of wavepackets, requiring the use of the dressed formalism. We construct the Hilbert space for QED in the dressed formalism as a representation of the canonical commutation relations of the photon creation/annihilation algebra, and argue that it splits into superselection sectors which correspond to eigenspaces of the generators of large gauge transformations.
In the second part of this thesis, we turn to applications of quantum information theoretic concepts in the AdS/CFT correspondence. In pure AdS, we find an explicit formula for the Ryu-Takayanagi (RT) surface for special subregions in the dual conformal field theory, whose entangling surface lie on a light cone. The explicit form of the RT surface is used to give a holographic proof of Markovicity of the CFT vacuum on a light cone. Relative entropy of a state on such special subregions is dual to a novel measure of energy associated with a timelike vector iiiflow between the causal and entanglement wedge. Positivity and monotonicity of relative entropy imply positivity and monotonicity of this energy, which yields a consistency conditions for solutions to quantum gravity.