# Resource Theories of Nonclassical Light

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## Abstract

**:**

## 1. Introduction

## 2. Preliminaries

## 3. The Resource Theoretical Framework

- $N\left(\rho \right)=0$ if $\rho \in \mathcal{C}$.
- (Monotonicity) $N\left(\rho \right)\ge N\left(\mathsf{\Phi}\right(\rho \left)\right)$ if $\mathsf{\Phi}\in \mathcal{O}$.
- (Convexity), i.e., $N\left({\sum}_{i}{p}_{i}{\rho}_{i}\right)\le {\sum}_{i}{p}_{i}N\left({\rho}_{i}\right)$ .

## 4. Resource Theory Based on Abstract Free Operations

## 5. Resource Theory Based on Linear Optical Operations

## 6. Convex Resource Theories of Non-Gaussianity

- a.
- Gaussian unitary operations ${U}_{G}$.
- b.
- Composition with a free state $\rho \otimes \sigma $, where $\sigma ={\sum}_{i}{p}_{i}{\sigma}_{G}^{i}$, ${p}_{i}$ is some probability distribution, and ${\sigma}_{G}^{i}$ is some Gaussian state.
- c.
- Partial trace of a subsystem.

## 7. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

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**MDPI and ACS Style**

Tan, K.C.; Jeong, H.
Resource Theories of Nonclassical Light. *Quantum Rep.* **2019**, *1*, 151-161.
https://doi.org/10.3390/quantum1020014

**AMA Style**

Tan KC, Jeong H.
Resource Theories of Nonclassical Light. *Quantum Reports*. 2019; 1(2):151-161.
https://doi.org/10.3390/quantum1020014

**Chicago/Turabian Style**

Tan, Kok Chuan, and Hyunseok Jeong.
2019. "Resource Theories of Nonclassical Light" *Quantum Reports* 1, no. 2: 151-161.
https://doi.org/10.3390/quantum1020014