What is nonlocal in counterfactual quantum communication?*

We revisit the “counterfactual quantum communication” of Salih et al., who claim that an observer “Bob” can send one bit of information to a second observer “Alice” without any physical particle traveling between them. We show that a locally conserved, massless current - specifically, a current of modular angular momentum, L_z mod 2$hbar$ - carries the one bit of information. We integrate the flux of L_z mod 2$hbar$ from Bob to Alice and show that it equals one of the two eigenvalues of L_z mod 2$hbar$, either 0 or $hbar$, thus precisely accounting for the one bit of information he sends her. We previously obtained this result using weak values of L_z mod 2$hbar$; here we do not use weak values.