Measurement of non-commuting spin components using spin-orbit interaction

We analyze the physical meaning of a possible experiment aimed at the simultaneous measurement of two non-commuting spin components. We demonstrate that switching of a strong spin-orbit interaction, e.g., in a solid state or a cold-atom system, for a short period of time simulates a simultaneous von Neumann measurement of spin components, $\sigma_x$ and $\sigma_y$. By mapping spin dynamics onto coordinate-space motion, such a measurement determines time averages of $\sigma_x$ and $\sigma_y$ which, unlike their instantaneous values, may be evaluated simultaneously to an arbitrary accuracy.