Spin-Bounded Correlations: Rotation Boxes Within and Beyond Quantum Theory.

How can detector click probabilities respond to spatial rotations around a fixed axis, in any possible physical theory? Here, we give a thorough mathematical analysis of this question in terms of "rotation boxes", which are analogous to the well-known notion of non-local boxes. We prove that quantum theory admits the most general rotational correlations for spins 0, 1/2, and 1, but we describe a metrological game where beyond-quantum resources of spin 3/2 outperform all quantum resources of the same spin. We prove a multitude of fundamental results about these correlations, including an exact convex characterization of the spin-1 correlations, a Tsirelson-type inequality for spins 3/2 and higher, and a proof that the general spin- correlations provide an efficient outer SDP approximation to the quantum set.

Entanglement-Asymmetry Correspondence for Internal Quantum Reference Frames.

In the quantization of gauge theories and quantum gravity, it is crucial to treat reference frames such as rods or clocks not as idealized external classical relata, but as internal quantum subsystems. In the Page-Wootters formalism, for example, evolution of a quantum system S is described by a stationary joint state of S and a quantum clock, where time dependence of S arises from conditioning on the value of the clock. Here, we consider (possibly imperfect) internal quantum reference frames R for arbitrary compact symmetry groups, and show that there is an exact quantitative correspondence between the amount of entanglement in the invariant state on RS and the amount of asymmetry in the corresponding conditional state on S.