# Binary Black Hole Information Loss Paradox and Future Prospects

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## Abstract

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## 1. Introduction

## 2. Background

## 3. Analysis

## 4. Gravitational Waves as a Context

## 5. Conclusions and Discussions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**This is the schematic representation of the process of the black hole evaporation for a binary system from a pseudo-density operator framework.

**Figure 2.**Experimental setup of the process. Here a Greenberger–Horne–Zeilinger (GHZ) state is generated by using two sets of $\beta -$barium borate (BBO) type-II crystal. Three sets of measurements are considered on photon A, B, where the measurements are considered for three different times (${t}_{1}$, ${t}_{2}$ and ${t}_{3}$ respectively) and a single measurement for the photon C.

**Figure 3.**Tomographic reconstruction of the reduced pseudo-density operator ${P}_{143}$ using the linear inversion method. The real part of the theoretical expectation (depicted by the true state in the plot) and the real part of the reduced pseudo-density operator is compared here.

**Figure 4.**Tomographic reconstruction of the reduced pseudo-density operator ${P}_{143}$ using the linear inversion method. The imaginary part of the theoretical expectation (depicted by the true state in the plot) and the imaginary part of the reduced pseudo-density operator is compared here.

**Figure 5.**Similar to Figure 3, state tomography reconstruction of the reduced pseudo-density operator ${P}_{143}$ is conducted using the projected linear inversion method. The real part of the theoretical expectation (depicted by the true state in the plot) and the reduced pseudo-density operator is compared.

**Figure 6.**Similar to Figure 4, state tomography reconstruction of the reduced pseudo-density operator ${P}_{143}$ is conducted using the projected linear inversion method. The imaginary part of the theoretical expectation (depicted by the true state in the plot) and the reduced pseudo-density operator is compared.

**Figure 7.**State tomography reconstruction of the reduced pseudo-density operator ${P}_{143}$ is conducted using the maximum likelihood estimation method. The real part of the theoretical expectation (depicted by the true state in the plot) and the reduced pseudo-density operator is compared.

**Figure 8.**State tomography reconstruction of the reduced pseudo-density operator ${P}_{143}$ is conducted using the maximum likelihood estimation method. The imaginary part of the theoretical expectation (depicted by the true state in the plot) and the reduced pseudo-density operator is compared.

**Figure 9.**The comparison of state tomographic reconstruction of the pseudo-density operator ${P}_{143}$ and the theoretical state (depicted by the true state in the plot) after the execution of the measurement.

**Figure 10.**State tomography reconstruction of the reduced pseudo-density operator ${P}_{453}$ is conducted using the maximum likelihood estimation method. The imaginary part of the theoretical expectation (depicted by the true state in the plot) and the reduced pseudo-density operator is compared.

**Figure 11.**State tomography reconstruction of the reduced pseudo-density operator ${P}_{453}$ is conducted using the maximum likelihood estimation method. The imaginary part of the theoretical expectation (depicted by the true state in the plot) and the reduced pseudo-density operator is compared.

**Figure 12.**Comparison of the two dimensional projection plot between the estimated state ${P}_{453}$ and the true state.

**Table 1.**Table showing the fidelity score F obtained from the three different methods used in the tomography used. Since F cannot exceed values of $0.5$ in the classical limit, it shows that there is true entanglement beyond the classical limit. In addition, the deviation in the models shows that better entanglement distillation could resolve this difference in values.

Method | Fidelity Score |
---|---|

Linear Inversion | 1.0 |

Projected Linear Inversion | 0.973 |

MLE | 0.999 |

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Mitra, A.; Chattopadhyay, P.; Paul, G.; Zarikas, V.
Binary Black Hole Information Loss Paradox and Future Prospects. *Entropy* **2020**, *22*, 1387.
https://doi.org/10.3390/e22121387

**AMA Style**

Mitra A, Chattopadhyay P, Paul G, Zarikas V.
Binary Black Hole Information Loss Paradox and Future Prospects. *Entropy*. 2020; 22(12):1387.
https://doi.org/10.3390/e22121387

**Chicago/Turabian Style**

Mitra, Ayan, Pritam Chattopadhyay, Goutam Paul, and Vasilios Zarikas.
2020. "Binary Black Hole Information Loss Paradox and Future Prospects" *Entropy* 22, no. 12: 1387.
https://doi.org/10.3390/e22121387