Abstract

Reference frames are essential in the description of physical phenomena. Often used implicitly, they appear as idealized classical systems. Following a more fundamental approach and considering them as physical systems subject to the laws of quantum mechanics, they become quantum reference frames (QRFs). A rigorous treatment of QRFs is indispensable both in the construction of a relational theory of quantum mechanics and of quantum gravity. Not only do the properties of QRFs give rise to numerous applications in quantum information; they are also expected to improve our understanding of observer-dependent settings such as the Wigner's friend experiment.

In this talk, we present a relational formalism based on the group and representation theoretic nature of reference frames. By identifying coordinate systems with elements of a symmetry group G, we define a general operator for reversibly transforming between QRFs associated to the group G. We explore the properties of this operator in different cases and show how it gives rise to transformations between coordinate systems which are `in a superposition' relative to other coordinate systems. Finally, we apply the relational formalism and the change of reference system developed in this work to the Wigner's friend thought experiment.