# Quantum trajectories for a system interacting with environment in a single photon state: counting and diffusive processes

## TL;DR

This paper derives quantum trajectories for a system interacting with a single-photon environment, capturing non-Markovian effects through continuous measurement models and providing formulas for photon counting probabilities.

## Contribution

It introduces a novel approach to model quantum trajectories with a single-photon environment using a discrete qubit series as an analogue of continuous modes, highlighting non-Markovian dynamics.

## Key findings

- Derived quantum trajectories for single-photon environment interactions.
- Established formulas for photon counting probabilities.
- Demonstrated non-Markovian effects due to initial correlations.

## Abstract

We derived quantum trajectories for a system interacting with the environment prepared in a continuous mode single photon state as the limit of discrete filtering model with an environment defined as series of independent qubits prepared initially in the entangled state being an analogue of a continuous mode state. The environment qubits interact with the quantum system and they are subsequently measured. The initial correlation between the bath qubits is the source of the non-Markovianity. The conditional evolutions of the quantum system for limit of the continuous in time observations together with the formulas for the photon counting probabilities are given.