What Is Nonlocal in Counterfactual Quantum Communication?

We revisit the "counterfactual quantum communication"of Salih et al. [1], 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, Lz mod 2ℏ - carries the one bit of information. We integrate the flux of Lz mod 2ℏ from Bob to Alice and show that it equals one of the two eigenvalues of Lz mod 2ℏ, either 0 or ℏ, thus precisely accounting for the one bit of information he sends her. We previously [2] obtained this result using weak values of Lz mod ℏ; here we do not use weak values.