# Statistical distribution of quantum correlation induced by multiple scattering in the disordered medium

## TL;DR

This paper investigates how superpositions and Gaussian versus non-Gaussian states influence quantum correlations in light scattered through disordered media, revealing differences in distribution and sign of correlations and their dependence on disorder strength.

## Contribution

It compares the effects of superpositions, Gaussian, and non-Gaussian states on quantum correlations in disordered media, highlighting how state type and disorder influence correlation properties.

## Key findings

- Superpositions and Fock states have similar average quantum correlations but different distributions.
- Non-Gaussian states can produce positive or negative quantum correlations, unlike Gaussian states.
- Increasing disorder strength generally enhances quantum correlation magnitude for multi-mode states.

## Abstract

For the quantum correlations between scattered modes in the disordered media, the previous works focus mainly on the cases where the inputs are non-superposed states, for instance, products of Fock states [Phys. Rev. Letts. 105 (2010) 090501]. A natural question that arises is how the superpositions affect the quantum correlations. Following this trail, the comparison between superpositions and products of Fock states is performed. It is found an interesting phenomenon that for the superposition and the corresponding product of Fock state (non-Gaussian states), their averaged quantum correlations are nearly same, whereas the distributions of their quantum correlations might be different. Therefore, superpositions may affect the distributions of the quantum correlations. In addition, to examine how the Gaussian states affect the quantum correlations, we compare the typical Gaussian states with the non-Gaussian states (superpositions and products of Fock states). It is discovered that the non-Gaussian-state input could result in the quantum correlation that is either positive or negative, depending on the number of the input modes and the number of the photons in each mode, whereas the Gaussian-state input always leads to the non-negative quantum correlation. Besides, it is demonstrated that with the increase of the disorder strength, the mean strength of the quantum correlation increases for multi-mode-state inputs (except for multi-mode-coherent-state inputs). These results may be useful to control and adjust the quantum properties of scattered modes after the quantized lights propagating through the disordered medium.