Abstract: 

 

Within holography a particularly important aspect of the correspondence between conformal field theories and bulk gravitational theories is the relationship between quantum information and geometry. Quantities that measure information or quantum entanglement in the CFT can often be related to geometric objects in the gravitational theory. By studying these geometric constructions, we can gain new insight into the structure of quantum information. For example, they can be used to provide simple derivations of otherwise complex properties and relations between measures. While bipartite entanglement can be fully captured by a single measure of information called the entanglement entropy the structure of entanglement between three or more parties, multi-partite entanglement, is much richer and less fully understood. In this talk I will describe a class of multi-partite measures called multi-invariants which are well suited to direct calculation in holographic theories. An important question involves understanding when gravitational constraints prevent the geometric constructions needed to represent these quantities. I will show that this phenomenon, known as bulk replica symmetry breaking, can be fully characterized based on properties of multi-invariants.

 

Time permitting I will also discuss recent work detailing how insight from holography can be used to inform the explicit calculation of multi-invariants for an important class of quantum states called stabilizer states.