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, L_z mod 2 ℏ —carries the one bit of information. We integrate the flux of L_z mod 2 ℏ from Bob to Alice and show that it equals one of the two eigenvalues of L_z mod 2 ℏ , 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 L_z mod ℏ ; here we do not use weak values.