What is nonlocal in counterfactual quantum communication?

TL;DR

This paper critically examines counterfactual quantum communication, demonstrating that a conserved current of modular angular momentum, rather than particles, carries the information between parties.

Contribution

The paper shows that modular angular momentum current, not particles, accounts for information transfer in counterfactual communication, providing a new physical understanding.

Findings

A conserved current of modular angular momentum carries the one bit of information.

The flux of $L_z$ mod 2$bar$ equals the eigenvalue encoding the bit.

The result is obtained without using weak values, unlike previous work.

Abstract

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$\hbar$ - 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 [2] obtained this result using weak values of $L_z$ mod 2$\hbar$; here we do not use weak values.