What does this equation mean?

What the covariance also does, though, is forbid the radiation from leaking coherence between different eigenspaces of $\hat J$ to an observer who has not independently fixed a frame. Kitaev, Mayers, and Preskill made the resource cost explicit: a superselection rule restricting accessible operations to those commuting with a group can be simulated away entirely if the two parties already share a suitable reference system, and cannot be worked around at all if they do not [ 11 ] . Absent such a shared frame, whatever the radiation reveals about g has to be extracted from the asymmetry of $\rho_{\mathrm{rad}}(g)$ relative to the group — a quantity that scrambling, left to its own devices, does not have any particular reason to concentrate quickly. The qubit’s logical content survives scrambling because nothing about being “close to |0$\rangle$ versus |1$\rangle$ ” is protected by a conservation law. The compass’s heading survives scrambling constrained by exactly the law that makes it meaningful in the first place, and that is a slower kind of survival.