Implementing Topological Entanglement as a Resource Theory

Abstract

Landau’s theory has been very successful on explaining phase transitions in many cases where a system suffers a change of its properties after symmetry breaking. However, for the case of topological ordered systems this is not necessarily true. The topological entanglement present on such systems remains invariant and undetectable from local measurements, thus slipping out from the scope of Landau’s symmetry breaking theory. The problem of characterizing such a state of many body systems has puzzled many physicists up to current days. Yet, some of its known properties are very promising for the application in fault tolerant quantum computing, like the famous case of the Toric code, or for understanding chiral spin liquids. In this talk we present an attempt on characterizing topological order of a system through resource theory, a theory whose mathematical foundations rely on category theory and which may provide a powerful way to implement it experimentally by introducing a “quantifier of resource” of the system’s topological order.