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Probability Distributions Describing Qubit-State Superpositions.

Margarita A Man'ko1, Vladimir I Man'ko1,2,3

  • 1Lebedev Physical Institute, Leninskii Prospect 53, Moscow 119991, Russia.

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We explore quantum mechanics using probability representations to analyze qubit states. This study reveals connections between entangled probability distributions and quantum properties.

Keywords:
Husimi functionWigner functionentangled probability distributionentropyprobability distributionsseparable probability distributiontomographic probability distribution

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Area of Science:

  • Quantum Mechanics
  • Quantum Information Theory

Background:

  • Quantum mechanics describes systems using wave functions and probabilities.
  • Qubit states are fundamental units in quantum computation.

Purpose of the Study:

  • To investigate qubit-state superpositions within the probability representation of quantum mechanics.
  • To analyze probability distributions for both separable and entangled qubit states.

Main Methods:

  • Utilizing the probability representation of quantum mechanics.
  • Examining superpositions of wave functions for separable and entangled (Bell) states of two qubits.

Main Results:

  • Characterized probability distributions for separable qubit states.
  • Established a connection between entangled probability distributions and the properties of Bell states.
  • Demonstrated how wave function superpositions relate to entangled probability structures.

Conclusions:

  • The probability representation offers insights into qubit state superpositions.
  • Entangled probability distributions exhibit unique properties linked to quantum entanglement.
  • This framework aids in understanding the structure of quantum information.