Aligning Reference Frames with Quantum States

Abstract

We analyze the problem of sending, in a single transmission, the information required to specify an orthogonal trihedron or reference frame through a quantum channel made out of $N$ elementary spins. We analytically obtain the optimal strategy, i.e., the best encoding state and the best measurement. For large $N$, we show that the average error goes to zero linearly in $1/N$. Finally, we discuss the construction of finite optimal measurements.