Framework for classifying logical operators in stabilizer codes

TL;DR

This paper introduces a framework to classify local and non-local properties of global operators in stabilizer codes, linking entanglement and non-local correlations through symmetries, with applications to topological order and entanglement measures.

Contribution

The paper presents a novel framework for classifying symmetries of global operators in stabilizer codes, bridging entanglement and non-local correlations analysis.

Findings

Analyzed global symmetries in topological order

Studied distribution of entanglement and entanglement entropy

Provided a method to relate entanglement with symmetries

Abstract

Entanglement, as studied in quantum information science, and non-local quantum correlations, as studied in condensed matter physics, are fundamentally akin to each other. However, their relationship is often hard to quantify due to the lack of a general approach to study both on the same footing. In particular, while entanglement and non-local correlations are properties of states, both arise from symmetries of global operators that commute with the system Hamiltonian. Here, we introduce a framework for completely classifying the local and non-local properties of all such global operators, given the Hamiltonian and a bi-partitioning of the system. This framework is limited to descriptions based on stabilizer quantum codes, but may be generalized. We illustrate the use of this framework to study entanglement and non-local correlations by analyzing global symmetries in topological order, distribution of entanglement and entanglement entropy.