Qubit state vector in probability representation of quantum mechanics

Review of probability representation of quantum mechanics where the system states are identified with fair probability distributions is presented. Examples of qubits and qutrits are given in detail. The explicit expressions of the qubit density matrices and qubit state vectors in terms of probabilit...

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Bibliographic Details
Main Authors: Chernega, Vladimir N., Man’ko, Olga V., Man’ko, Vladimir I.
Format: Conference Proceeding
Language:English
Subjects:
Density
Hamiltonian functions
Mathematical analysis
Probability
Quantum mechanics
Quantum physics
Qubits (quantum computing)
Random variables
Representations
State vectors
Wave functions
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Summary:Review of probability representation of quantum mechanics where the system states are identified with fair probability distributions is presented. Examples of qubits and qutrits are given in detail. The explicit expressions of the qubit density matrices and qubit state vectors in terms of probabilities of dichotomic random variables are discussed. The wave function of a qubit state, and its phase which is not contained in the density matrix of the state, are expressed in terms of the dichotomic probabilities. The generalisation of the probability representation to the case of qudit state is considered. The Schrödinger–like equation for spectra of Hermitian and non Hermitian Hamiltonians is written in the new form of equation for the dichotomic probabilities.
ISSN:0094-243X
1551-7616
DOI:10.1063/5.0055097