Counterfactual computation revisited

TL;DR

This paper revisits the concept of counterfactual computation, clarifies the physical interpretation of a specific protocol, and proposes a modified definition to better capture its counterfactual nature.

Contribution

It offers a more physically adequate definition of counterfactual computation and clarifies the counterfactuality of the chained-Zeno protocol.

Findings

The protocol is counterfactual under the new definition.

The existing 'history tracking' method is inadequate.

A modified definition better captures the physics involved.

Abstract

Mitchison and Jozsa recently suggested that the "chained-Zeno" counterfactual computation protocol recently proposed by Hosten et al. is counterfactual for only one output of the computer. This claim was based on the existing abstract algebraic definition of counterfactual computation, and indeed according to this definition, their argument is correct. However, a more general definition (physically adequate) for counterfactual computation is implicitly assumed by Hosten et. al. Here we explain in detail why the protocol is counterfactual and how the "history tracking" method of the existing description inadequately represents the physics underlying the protocol. Consequently, we propose a modified definition of counterfactual computation. Finally, we comment on one of the most interesting aspects of the error-correcting protocol.