# Asymmetry of Quantum Correlations Decay in Nonlinear Bosonic System

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## Abstract

**:**

## 1. Introduction

## 2. The Model

## 3. Entanglement Decay under Dissipation Channel Combinations

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Fidelity between the numerically obtained wave function describing the whole two-mode system in an extended basis and the truncated wave function for the subspace ${\left\{\right|0\rangle}_{a}{|0\rangle}_{b}{;|0\rangle}_{a}{|2\rangle}_{b}{;|2\rangle}_{a}{|0\rangle}_{b}{;|2\rangle}_{a}{|2\rangle}_{b};\}$ — solid line, and for the subspace ${\left\{\right|1\rangle}_{a}{|1\rangle}_{b}{;|1\rangle}_{a}{|2\rangle}_{b}{;|2\rangle}_{a}{|1\rangle}_{b}{;|2\rangle}_{a}{|2\rangle}_{b};\}$ — dashed line. The initial state of the system is a two-photon state ${|0\rangle}_{a}{|2\rangle}_{b}$, $\gamma =0$; $\u03f5=\alpha =\chi /100$.

**Figure 2.**Visualization of different location of noise in the model of the symmetric coupled oscillatory system.

**Figure 3.**Negativities for 2-qubit subspaces—${N}_{0220}$ (solid line) and ${N}_{1221}$ (dashed line) versus time scaled in $1/\chi $ units for combinations of damping channels. In (

**a**) and (

**c**) the mode a is exposed to the amplitude damping channel and mode b into the phase-damping channel. In (

**b**) and (

**d**) the channels are swapped. The initial state of the system is a two-photon one ${|0\rangle}_{a}{|2\rangle}_{b}$, $\gamma =\u03f5=\alpha =\chi /100$ for (

**a**) and (

**b**); $\gamma =\u03f5=\chi /100$ and $\alpha =\chi /25$ for (

**c**) and (

**d**).

**Figure 4.**Fidelities for obtaining the entangled states for $\gamma =\u03f5=\chi /100$, $\alpha =\chi /25$ and the initial state ${|0\rangle}_{a}{|2\rangle}_{b}$. In (

**a**) the mode a is exposed to the amplitude damping channel and the mode b to the phase-damping channel. In (

**b**) the channels are swapped. ${|B\rangle}_{1}$—solid line; ${|B\rangle}_{2}$—dashed line; ${|B\rangle}_{3}$—dashed-dotted line and ${|B\rangle}_{4}$—dotted line.

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**MDPI and ACS Style**

Kowalewska-Kudłaszyk, A.; Chimczak, G.
Asymmetry of Quantum Correlations Decay in Nonlinear Bosonic System. *Symmetry* **2019**, *11*, 1023.
https://doi.org/10.3390/sym11081023

**AMA Style**

Kowalewska-Kudłaszyk A, Chimczak G.
Asymmetry of Quantum Correlations Decay in Nonlinear Bosonic System. *Symmetry*. 2019; 11(8):1023.
https://doi.org/10.3390/sym11081023

**Chicago/Turabian Style**

Kowalewska-Kudłaszyk, Anna, and Grzegorz Chimczak.
2019. "Asymmetry of Quantum Correlations Decay in Nonlinear Bosonic System" *Symmetry* 11, no. 8: 1023.
https://doi.org/10.3390/sym11081023