Probability Representation of Quantum States

Entropy

OlgaV. Man’ko¹  VladimirI. Man’ko¹ 

[1] Lebedev Physical Institute, Russian Academy of Sciences, Leninskii Prospect 53, 119991 Moscow, Russia;

关键词: probability distribution;    tomography;    quantizer;    dequantizer;    star–product;    qubit;   

DOI  :  10.3390/e23050549

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown