Quantum reference frame transformations as symmetries and the paradox of the third particle Marius Krumm, co-authors: Philipp A. Hoehn and Markus P. Mueller

In a quantum world, reference frames are ultimately quantum systems too — but what does it mean to “jump into the perspective of a quantum particle”? We show that quantum reference frame (QRF) transformations appear naturally as symmetries of simple physical systems. This allows us to rederive and generalize known QRF transformations within an alternative, operational framework, and to shed new light on their structure and interpretation. We give an explicit description of the observables that are measurable by agents constrained by such quantum symmetries, and apply our results to the ‘paradox of the third particle’. We argue that it can be reduced to the question of how to relationally embed fewer into more particles. This leads us to a generalization of the partial trace which arguably resolves the paradox, and it uncovers important structures of constraint quantization within a simple quantum information setting, such as relational observables which are key in this resolution.