# Post-Selection and Counterfactual Communication

## TL;DR

This paper critically examines quantum counterfactual communication protocols that rely on post-selection, arguing that such protocols are not genuinely counterfactual because post-selection eliminates information flow and the violation strength diverges.

## Contribution

The paper demonstrates that post-selection removes Fisher information flow in quantum protocols and shows classical post-selected protocols can be counterfactual, questioning the genuineness of quantum counterfactual communication.

## Key findings

- Post-selection eliminates Fisher information flow.
- Classical post-selected protocols can be counterfactual.
- Quantum protocols' violation strength diverges faster than discard probability.

## Abstract

A recent quantum protocol for counterfactual communication [Y. Aharonov and L. Vaidman, Phys. Rev. A 99, 010103(R), 2019] relies on post-selection to eliminate the weak trace in the transmission channel. We show that the post-selection in this protocol also eliminates the flow of Fisher information from transmitter to receiver. However, we also show that a classical communication protocol with post-selection can be counterfactual. Hence, we argue that post-selection should not be allowed in genuine counterfactual communication. In the quantum counterfactual communication protocol, the probability of discarding an event by post-selection tends to zero with an increasing number of ideal optical components. But the counterfactual violation strength tends to infinity at a faster rate. Consequently, the quantum protocol is not counterfactual proper.