An introduction to quantum reference frames and their application in gauge theory and gravity

Quantum reference frames (QRFs) are a universal tool for dealing with symmetries in quantum theory. While they originated in the foundations of quantum theory and quantum information, they are particularly useful in theories with gauge symmetries, where they define a split between redundant and non-redundant information. Broadly, QRFs correspond to the degrees of freedom that one fixes in a gauge fixing procedure or, equivalently, employs to dress non-invariant operators into invariant ones.
In this lecture, I will introduce QRFs and explain how their identification in gauge systems as frames for the pertinent gauge group leads to novel relational insights into gauge-invariant descriptions, core of which is a covariance under changes of QRFs. This leads to a QRF-dependence of entanglement, thermal properties and more generally of gauge-invariant definitions of subsystem partitions. For illustration, I will then apply this to perturbative quantum gravity and clarify how the recent story about “observers” in gravitational algebras by Witten et al. is one about QRFs.
Depending on interest and time, I may also explain what edge modes and finite regions in gauge theory and gravity have to do with QRFs and/or how QRFs permit to establish a correspondence between (group-based) quantum error correction and gauge theories.