Optimal Measurements for Relative Quantum Information

We provide optimal measurement schemes for estimating relative parameters of the quantum state of a pair of spin systems. Specifically, we consider the task of estimating the angle between the spin directions of a pair of systems in SU(2) coherent states. We prove that the optimal measurements are non-local, in the sense that they cannot be achieved by local operations and classical communication. We also demonstrate that in the limit where one or both of the spins becomes macroscopic, our results reproduce those that are obtained by treating the macroscopic spin classically