# Robust Free-Space Optical Communication Utilizing Polarization for the Advancement of Quantum Communication

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Experiment

#### 2.2. Simulation

## 3. Results

## 4. Discussion

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

DOP | Degree of polarization |

FSO | Free-space optics |

SOP | State of polarization |

LP | Linear polarizer |

BS | Beam splitter |

QWP | Quarter wave plate |

HWP | Half wave plate |

Det. | Detector |

VND | Variable neutral density |

## Appendix A. Simulation of Atmospheric Turbulence

**Figure A1.**Measured DOP of the output states through simulated atmospheric turbulence compared to the measured DOP of the input states for different arbitrary partially polarized states. (

**a**) The output DOP with respect to the input DOP for an arbitrary basis. Input and output DOP are equal at the black like ($y=x$). Atmospheric turbulence simulation results are shown in blue. The error bars represent 99% confidence interval. We see DOP is preserved for arbitrary states. (

**b**) Arbitrary input and output states in the Poincare sphere representation. Atmospheric turbulence simulation input states are red squares, atmospheric turbulence simulation output states are blue circles. On the Poincare sphere: D = diagonal, A = anti-diagonal, L = left, R = right, V = vertical, H = horizontal.

## Appendix B. Intensity Distribution

**Figure A2.**Histogram of intensities for initially vertically polarized light with $\mathrm{DOP}=0.8$ obtained from (

**a**) simulation and (

**b**) experiment. The simulated data is cutoff above $I=2$ and below $I=0.03$ to better reflect the dynamic range of the detector used in the experimental setup while preserving the structure of the random fluctuations. The experiment data corresponds to the measurement of $I({0}^{\circ},{90}^{\circ})$.

**Figure A3.**Probability density vs the normalized intensity for (

**a**) simulation and (

**b**) experimental results. In each plot, we include the fitted probability density functions of the gamma distribution (orange) and the log-normal distributions (black dashed).

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**Figure 1.**Experimental setup used to generate different polarization states, pass them through experimentally generated turbulence, and perform tomography measurements. Abbreviations: PBS = polarizing beamsplitter, QWP = quarter-wave plate, HWP = half-wave plate, P = linear polarizer, VND = variable neutral density filter, BS = 50:50 non-polarizing beamsplitter, Det. = photodetector.

**Figure 2.**Measured DOP of the output states through underwater bubbles compared to the measured DOP of the input states for different partially polarized states. Input and output DOP are equal at the black like ($y=x$). Experimentally obtained data is shown in red and simulation results are shown in blue. The error bars represent 99% confidence interval.

**Figure 3.**Input and output states in the Poincare sphere representation. Experimental input states are orange triangles, experimental output states are green diamonds, stationary bubbles simulation input states are red squares, stationary bubbles simulation output states are blue circles. On the Poincare sphere: D = diagonal, A = anti-diagonal, L = left, R = right, V = vertical, H = horizontal.

**Figure 4.**Measured DOP of the output states through underwater turbulence compared to the measured DOP of the input states for different arbitrary partially polarized states. Experimental and stationary bubbles simulation results are compared. (

**a**) The output DOP with respect to the input DOP for an arbitrary basis. Input and output DOP are equal at the black like ($y=x$). Experimentally obtained data is shown in red and stationary bubbles simulation results are shown in blue. The error bars represent 99% confidence interval. We see DOP is preserved for arbitrary states. (

**b**) Arbitrary input and output states in the Poincare sphere representation. Experimental input states are orange triangles, experimental output states are green diamonds, stationary bubbles simulation input states are red squares, stationary bubbles simulation output states are blue circles. On the Poincare sphere: D = diagonal, A = anti-diagonal, L = left, R = right, V = vertical, H = horizontal.

Parameter | Symbol | Value |
---|---|---|

Power transmitted | ${P}_{trans}$ | ≈24 dBm |

Transmitter gain | ${G}_{trans}$ | ≈0 dB |

Transmitter loss | ${L}_{trans}$ | ≈15 to 18 dB |

Free-space loss | ${L}_{fs}$ | ≈0 dB |

Turbulence related loss | ${L}_{turb}$ | ≈13 dB |

Receiver gain | ${G}_{rec}$ | ≈0 dB |

Receiver loss | ${G}_{rec}$ | ≈0 to 20 dB |

**Table 2.**Measured mean normalized Stokes parameters of the input and output partially polarized states on the horizontal/vertical axis through experimental underwater turbulence.

State | ${\mathit{s}}_{1}/{\mathit{s}}_{0}$ | ${\mathit{s}}_{2}/{\mathit{s}}_{0}$ | ${\mathit{s}}_{3}/{\mathit{s}}_{0}$ | DOP | ||||
---|---|---|---|---|---|---|---|---|

Input | Output | Input | Output | Input | Output | Input | Output | |

0 | 0.09 | 0.14 | −0.04 | 0.01 | −0.04 | −0.05 | 0.11 | 0.15 |

1 | 0.36 | 0.39 | −0.05 | −0.07 | −0.03 | −0.07 | 0.36 | 0.40 |

2 | 0.53 | 0.55 | −0.04 | −0.08 | −0.02 | −0.10 | 0.53 | 0.57 |

3 | 0.74 | 0.71 | −0.05 | −0.03 | −0.02 | −0.06 | 0.74 | 0.72 |

4 | 0.99 | 0.92 | −0.06 | −0.10 | −0.02 | −0.08 | 0.99 | 0.93 |

**Table 3.**Measured mean normalized Stokes parameters of the input and output arbitrary partially polarized states through experimental underwater turbulence.

State | ${\mathit{s}}_{1}/{\mathit{s}}_{0}$ | ${\mathit{s}}_{2}/{\mathit{s}}_{0}$ | ${\mathit{s}}_{3}/{\mathit{s}}_{0}$ | DOP | ||||
---|---|---|---|---|---|---|---|---|

Input | Output | Input | Output | Input | Output | Input | Output | |

0 | 0.03 | 0.04 | 0.06 | −0.02 | 0.05 | 0.10 | 0.08 | 0.11 |

1 | 0.08 | 0.11 | −0.11 | −0.15 | 0.29 | 0.33 | 0.32 | 0.38 |

2 | 0.12 | 0.13 | −0.32 | −0.25 | 0.43 | 0.43 | 0.55 | 0.51 |

3 | 0.18 | 0.17 | −0.45 | −0.36 | 0.62 | 0.68 | 0.79 | 0.79 |

4 | 0.25 | 0.25 | −0.43 | −0.47 | 0.78 | 0.73 | 0.93 | 0.91 |

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## Share and Cite

**MDPI and ACS Style**

Savino, N.; Leamer, J.; Saripalli, R.; Zhang, W.; Bondar, D.; Glasser, R.
Robust Free-Space Optical Communication Utilizing Polarization for the Advancement of Quantum Communication. *Entropy* **2024**, *26*, 309.
https://doi.org/10.3390/e26040309

**AMA Style**

Savino N, Leamer J, Saripalli R, Zhang W, Bondar D, Glasser R.
Robust Free-Space Optical Communication Utilizing Polarization for the Advancement of Quantum Communication. *Entropy*. 2024; 26(4):309.
https://doi.org/10.3390/e26040309

**Chicago/Turabian Style**

Savino, Nicholas, Jacob Leamer, Ravi Saripalli, Wenlei Zhang, Denys Bondar, and Ryan Glasser.
2024. "Robust Free-Space Optical Communication Utilizing Polarization for the Advancement of Quantum Communication" *Entropy* 26, no. 4: 309.
https://doi.org/10.3390/e26040309