Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:quant-ph/0608251

Probability Representation of Quantum Mechanics: Comments and Bibliography

Vladimir I. Man’ko, Oleg V. Pilyavets, Vadim Zborovskii

Published Aug 31, 2006• 0 citations
arXivHTMLPDF

Abstract

The probability representation of states in standard quantum mechanics where the quantum states are associated with fair probability distributions (instead of wave function or density matrix) is shortly commented and bibliography related to the probability representation is given.
DOI
10.48550/arxiv.quant-ph/0608251

Related papers

Probability Representation of Quantum States

Olga V. Man’ko, Vladimir I. Man’ko

The review of new formulation of conventional quantum mechanics where the quantum states are identified with probability distributions is presented. The invertible map of density operators and wave functions onto the probability distributions describing the quantum states in quantum mechanics is constructed both for systems with continuous variables and systems with discrete variables by using the Born's rule and recently suggested method of dequantizer-quantizer operators. Examples of discussed probability representations of qubits (spin-1/2, two-level atoms), harmonic oscillator and free particle are studied in detail. Schrödinger and von Neumann equations, as well as equations for the evolution of open systems, are written in the form of linear classical-like equations for the probability distributions determining the quantum system states. Relations to phase-space representation of quantum states (Wigner functions) with quantum tomography and classical mechanics are elucidated.

Entropy•Apr 29, 2021•43 citations

Qubit state vector in probability representation of quantum mechanics

Vladimir N. Chernega, Olga V. Man’ko, Vladimir I. Man’ko

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.

AIP conference proceedings•Jan 1, 2021•0 citations

Standard quantum mechanics with a probability distribution instead of a wave function

Vladimir I. Man’ko

PAN•Oct 1, 1998•0 citations

Probability and quantum mechanics

Daniel J. Velleman

We discuss the use of probability theory in quantum mechanics, and suggest that there are some interpretations of quantum mechanics in which probabilities may be used inappropriately.

American Journal of Physics•Nov 1, 1998•4 citations

Probability Instead of Wave Function and Bell Inequalities as Entanglement Criterion

Vladimir I. Man’ko, Guillaume Adenier, Andrei Yu. Khrennikov +3 more

Review of the probability representation of quantum mechanics, in which a fair probability distribution is used instead of the density matrix or wave function to describe quantum states is presented. Bell inequalities are formulated as properties of joint probability distributions describing the states of multipartite spin systems in the probability representation. Probability distributions depending on extra parameters are discussed in the connection with problems of classical and quantum statistical mechanics, where these distributions can be considered in the context of non‐Kolmogorov probability theory.

AIP conference proceedings•Jan 1, 2007•6 citations

Canonical transforms, quantumness and probability representation of quantum mechanics

Margarita A. Man’ko, Vladimir I. Man’ko, Kurt B. Wolf +3 more

The linear canonical transforms of position and momentum are used to construct the tomographic probability representation of quantum states where the fair probability distribution determines the quantum state instead of the wave function or density matrix. The example of Moshinsky shutter problem is considered.

arXiv:1103.0193•AIP conference proceedings•Jan 1, 2010•0 citations
The review of new formulation of conventional quantum mechanics where the quantum states are identified with probability distributions is presented. The invertible map of density operators and wave functions onto the probability distributions describing the quantum states in quantum mechanics is constructed both for systems with continuous variables and systems with discrete variables by using the Born's rule and recently suggested method of dequantizer-quantizer operators. Examples of discussed probability representations of qubits (spin-1/2, two-level atoms), harmonic oscillator and free particle are studied in detail. Schrödinger and von Neumann equations, as well as equations for the evolution of open systems, are written in the form of linear classical-like equations for the probability distributions determining the quantum system states. Relations to phase-space representation of quantum states (Wigner functions) with quantum tomography and classical mechanics are elucidated.
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.
Review of the probability representation of quantum mechanics, in which a fair probability distribution is used instead of the density matrix or wave function to describe quantum states is presented. Bell inequalities are formulated as properties of joint probability distributions describing the states of multipartite spin systems in the probability representation. Probability distributions depending on extra parameters are discussed in the connection with problems of classical and quantum statistical mechanics, where these distributions can be considered in the context of non‐Kolmogorov probability theory.