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PT
-Symmetric Qubit-System States in the Probability Representation of Quantum Mechanics

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## Abstract

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## 1. Introduction

## 2. Two-Level Atom States

## 3. Schrödinger’s Equation for Energy Levels in the Probability Representation

## 4. Probability Representation of the Eigenvalue Equations for Generic Non-Hermitian Hamiltonians of Qubit Systems

## 5. The Schrödinger Equation for States with Eigenvalues of Energy as Equations for Eigenvectors with Components—Probabilities Determining Qubit States

## 6. A Probability Representation for the Non-Hermitian Hamiltonian Eigenvalue Equation of the Qutrit State

## 7. An Example of a Non-Hermitian Hamiltonian with $\mathcal{PT}$-Symmetry

## 8. The Superposition Principle and $\mathcal{PT}$-Symmetric States

## 9. Qubit States with Broken $\mathcal{PT}$-Symmetry

## 10. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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Chernega, V.N.; Man’ko, M.A.; Man’ko, V.I.
*Symmetry* **2020**, *12*, 1702.
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Chernega VN, Man’ko MA, Man’ko VI.
*Symmetry*. 2020; 12(10):1702.
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Chernega, Vladimir N., Margarita A. Man’ko, and Vladimir I. Man’ko.
2020. "*Symmetry* 12, no. 10: 1702.
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