Visibility Stokes parameters as a foundation for quantum information science with undetected photons

TL;DR

This paper introduces visibility Stokes parameters for undetected photons, providing a new, intuitive framework for quantum state tomography and potentially enabling adaptation of quantum protocols to undetected photon systems.

Contribution

It formulates a set of visibility Stokes parameters for undetected photons, offering a consistent and intuitive approach to quantum measurement and state reconstruction.

Findings

Visibility Stokes parameters effectively quantify polarization of undetected photons.

The framework improves understanding of measurement processes involving undetected photons.

Potential to adapt existing quantum information protocols for undetected photon systems.

Abstract

The framework of measurement operators plays a fundamental role in extracting information about quantum systems. Recently, techniques based on induced coherence have been developed to access the same information for undetected photons. However, there has been a lack of consistent reformulation of quantum operators for these techniques. In this work, we introduce a set of parameters that quantify the polarization of undetected photons based on measured visibilities. Given their similarity to classical counterparts, we refer to them as visibility Stokes parameters. We apply these parameters and the corresponding quantum operators to the problem of quantum state tomography, thoroughly analyzing the environment of undetected photons and its role in the reconstruction process. Because these parameters provide a more intuitive and consistent understanding of the measurement process, we believe that some established quantum information protocols could be adapted for undetected photons.