Global asymmetry of many-qubit correlations: A lattice gauge theory approach

TL;DR

This paper introduces a gauge theory-inspired measure called 'twist' to quantify global asymmetry in many-qubit correlations, linking quantum information with lattice gauge theory concepts.

Contribution

It establishes a novel framework connecting quantum correlations with gauge field theory, using Wilson loops and holonomy to characterize entanglement asymmetry.

Findings

Defined 'twist' as a Wilson loop measure of correlation holonomy.

Identified the gauge group as Lorentz transformations.

Provided analytical examples of twisted and untwisted three-qubit states.

Abstract

We introduce a novel bridge between the familiar gauge field theory approaches used in many areas of modern physics such as quantum field theory and the SLOCC protocols familiar in quantum information. Although the mathematical methods are the same the meaning of the gauge group will be different. The measure we introduce, `twist', is constructed as a Wilson loop from a correlation induced holonomy. The measure can be understood as the global asymmetry of the bipartite correlations in a loop of three or more qubits; if the holonomy is trivial (the identity matrix), the bipartite correlations can be globally untwisted using general local qubit operations, the gauge group of our theory, which turns out to be the group of Lorentz transformations familiar from special relativity. If it is not possible to globally untwist the bipartite correlations in a state globally using local operations, the twistedness is given by a non-trivial element of the Lorentz group, the correlation induced holonomy. We provide several analytical examples of twisted and untwisted states for three qubits, the most elementary non-trivial loop one can imagine.