What does this equation mean?

Into this old hole go two systems. The first, A , is a two-dimensional qubit prepared in an arbitrary, unknown state and coupled to nothing the hole’s own symmetries track — a spectator, chosen so that its recovery is the cleanest possible test of the Hayden-Preskill mechanism on its own terms. The second, C , is a compass: a physical carrier prepared in a state |$\psi(g)$$\rangle$ that transforms under a one-parameter group of rotations generated by a Hermitian charge $\hat J$ , the same charge the hole’s own angular momentum is built from, $|\psi(g)\rangle = e^{-ig\hat J/\hbar}\,|\psi(0)\rangle, \qquad g \in [0,2\pi)$. g is an angle: dimensionless, periodic, and physically read as “which way the compass points” relative to the hole’s spin axis. $\hat J$ carries units of action (joule-seconds), so g$\hat J$/$\hbar$ is dimensionless, as an exponent must be. Nothing about this setup is exotic — a large-spin coherent state pointing along a direction is a textbook carrier of exactly this kind of information [ 10 ] .