Speed excess and total acceleration: a kinematical approach to entanglement

Abstract The total variance of a spin state is defined as the average of the variances of spin projection measurements along three orthogonal axes. We show that this quantity also gives the squared rotational speed of the state in projective space, averaged over all rotation axes. We compute the addition law, under system composition, for this quantity and find that, in the case of separable states, it is of simple pythagorean form. In the presence of entanglement, we find that the composite state ‘rotates faster than its parts’, thus unveiling a kinematical origin for the correlation of total variance with entanglement. We analyze a similar definition for the acceleration of a state under rotations, for both pure and mixed states, and probe numerically its relation with a wide array of entanglement related measures.