# The quantum regression theorem for out-of-time-ordered correlation functions

## TL;DR

This paper extends the quantum regression theorem to compute out-of-time-ordered correlation functions in open quantum systems, revealing their natural occurrence in optical detection and enabling analysis of photon fluctuations.

## Contribution

The authors derive a new extension of the quantum regression theorem for out-of-time-ordered correlations in Markovian systems, bridging theory and optical detection applications.

## Key findings

- Out-of-time-ordered correlations naturally appear in optical detection schemes.
- The extended theorem allows calculation of photon counting fluctuations.
- Application to quantum light sources demonstrates practical relevance.

## Abstract

We derive an extension of the quantum regression theorem to calculate out-of-time-order correlation functions in Markovian open quantum systems. While so far mostly being applied in the analysis of many-body physics, we demonstrate that out-of-time-order correlation functions appear naturally in optical detection schemes with interferometric delay lines, and we apply our extended quantum regression theorem to calculate the non-trivial photon counting fluctuations in split and recombined signals from a quantum light source.