Counterfactuality, back-action, and information gain in multi-path interferometers

TL;DR

This paper investigates quantum counterfactual effects in multi-path interferometers, quantifying how absorbers influence output statistics and demonstrating the quantum advantage over classical protocols through information gain and quasiprobability analysis.

Contribution

It introduces a quantitative framework for counterfactual effects, including the concept of counterfactual gain and the role of Kirkwood-Dirac quasiprobabilities in multi-path interferometers.

Findings

Quantum counterfactual effects are linked to negative Kirkwood-Dirac quasiprobabilities.

Counterfactual gain can be separated into semi-classical and quantum components.

Back-action effects, not just particle removal, drive quantum counterfactual phenomena.

Abstract

The presence of an absorber in one of the paths of an interferometer changes the output statistics of that interferometer in a fundamental manner. Since the individual quantum particles detected at any of the outputs of the interferometer have not been absorbed, any non-trivial effect of the absorber on the distribution of these particles over these paths is a counterfactual effect. Here, we quantify counterfactual effects by evaluating the information about the presence or absence of the absorber obtained from the output statistics, distinguishing between classical and quantum counterfactual effects. We identify the counterfactual gain which quantifies the advantage of quantum counterfactual protocols over classical counterfactual protocols, and show that this counterfactual gain can be separated into two terms: a semi-classical term related to the amplitude blocked by the absorber, and a Kirkwood-Dirac quasiprobability assigning a joint probability to the blocked path and the output port. A negative Kirkwood-Dirac term between a path and an output port indicates that inserting the absorber into that path will have a focussing effect, increasing the probability of particles arriving at that output port, resulting in a significant enhancement of the counterfactual gain. We show that the magnitude of quantum counterfactual effects cannot be explained by a simple removal of the absorbed particles, but originates instead from a well-defined back-action effect caused by the presence of the absorber in one path, on particles in other paths.