Operational Quantum Reference Frame Transformations

We provide a general, operational, and rigorous basis for quantum reference frames and their transformations using covariant positive operator valued measures to represent frame observables. The framework holds for locally compact groups and differs from all prior proposals for frame changes, being built around the notion of operational equivalence, in which states that cannot be distinguished physically are identified. This allows for the construction of the space of (invariant) relative observables and the convex set of relative states as dual objects. By demanding a further equivalence relation on the relative states which takes into account the nature of the frames, we provide a quantum…