Three approaches for analyzing the counterfactuality of counterfactual protocols

TL;DR

This paper evaluates three methods for analyzing the counterfactuality of communication protocols, finding that classical analysis is flawed, while the weak trace and Fisher information criteria agree and highlight the importance of postselection.

Contribution

It introduces and compares three approaches for assessing counterfactuality, emphasizing the role of postselection and discussing experimental modifications.

Findings

Classical analysis leads to contradictions and should be abandoned.

Weak trace and Fisher information criteria agree on counterfactuality assessments.

Postselection is essential for counterfactual communication protocols.

Abstract

Counterfactual communication protocols are analysed using three approaches: a classical argument, the weak trace criterion, and the Fisher information criterion. It is argued that the classical analysis leads to contradiction and should therefore be abandoned. The weak trace and Fisher information criteria are shown to agree about the degree of counterfactuality of communication protocols involving postselection. It is argued that postselection is a necessary ingredient of counterfactual communication protocols. Coherent interaction experiments, as well as a recently introduced modification of counterfactual communication setups which eliminates the weak trace, are discussed.