We address the problem of measuring the relative angle between two “quantum axes” made out of $N_1$ and $N_2$ spins. Closed forms of our fidelitylike figure of merit are obtained for an arbitrary number of parallel spins. The asymptotic regimes of large $N_1$ and/or $N_2$ are discussed in detail. The extension of the concept “quantum axis” to more general situations is addressed. We give optimal strategies when the first quantum axis is made out of parallel spins whereas the second is a general state made out of two spins.

• Received 11 October 2005

DOI:https://doi.org/10.1103/PhysRevA.73.022341