Location
QNC 2101
Candidate
Kelly Wurtz | Applied Mathematics, University of Waterloo
Title
Harvesting entanglement on the lattice and in holography
Abstract
Entanglement in quantum field theory is difficult not only to calculate but also to interpret: continuum entanglement entropies are ultraviolet divergent, and holographic entanglement measures do not by themselves specify what a local experiment can access. This thesis studies field entanglement through localised probes: finite quantum systems coupled to quantum fields whose final states contain accessible correlations. The first part studies a free scalar field on a harmonic lattice. For a given spatial region of the field, the reduced vacuum decomposes into Williamson normal modes that isolate the entanglement between the subregion and its complement. The most entangled modes are shown to be optimal targets for extraction into detector degrees of freedom, and detector couplings are constructed that realise this extraction by swapping selected field modes with probes. The extraction is then assigned an energetic cost by putting selected modes in their vacuum states and evaluating the change in the original lattice Hamiltonian. Numerically, both the extracted entropy and the energy cost obey area-law behaviour over the regimes studied.
The second part turns to conformal field theories and their AdS holographic duals. First, we couple Unruh-Dewitt detectors to scalar primary operators in a conformal field theory, and study their ability to harvest entanglement. At leading perturbative order, the detector state is fixed by the universal CFT two-point function, allowing harvested negativity and mutual information to be studied as functions of scaling dimension and detector geometry. In holographic CFTs, the bulk dual also provides an operational way to separate genuine harvesting from causal communication.
The final part uses HKLL reconstruction to describe bulk detector interactions in anti-de Sitter space from the boundary perspective. A local bulk detector is represented on the boundary by a nonlocal, time-dependent coupling whose smearing is fixed by the reconstruction kernel.