Superposition Principle and Born’s Rule in the Probability Representation of Quantum States

Igor Ya. Doskoch; Margarita A. Man’ko

doi:10.3390/quantum1020013

journal article Open Access Sep 26, 2019

Superposition Principle and Born’s Rule in the Probability Representation of Quantum States

Igor Ya. Doskoch

Margarita A. Man’ko

Quantum Reports Vol. 1 No. 2 pp. 130-150 · MDPI AG

View at Publisher Save 10.3390/quantum1020013

Abstract

The basic notion of physical system states is different in classical statistical mechanics and in quantum mechanics. In classical mechanics, the particle system state is determined by its position and momentum; in the case of fluctuations, due to the motion in environment, it is determined by the probability density in the particle phase space. In quantum mechanics, the particle state is determined either by the wave function (state vector in the Hilbert space) or by the density operator. Recently, the tomographic-probability representation of quantum states was proposed, where the quantum system states were identified with fair probability distributions (tomograms). In view of the probability-distribution formalism of quantum mechanics, we formulate the superposition principle of wave functions as interference of qubit states expressed in terms of the nonlinear addition rule for the probabilities identified with the states. Additionally, we formulate the probability given by Born’s rule in terms of symplectic tomographic probability distribution determining the photon states.

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Details

Published: Sep 26, 2019
Vol/Issue: 1(2)
Pages: 130-150
License: View

Authors

I

Igor Ya. Doskoch

Lebedev Physical Institute, Leninskii Prospect 53, Moscow 119991, Russia

M

Margarita A. Man’ko

Lebedev Physical Institute, Leninskii Prospect 53, Moscow 119991, Russia

Cite This Article

Igor Ya. Doskoch, Margarita A. Man’ko (2019). Superposition Principle and Born’s Rule in the Probability Representation of Quantum States. Quantum Reports, 1(2), 130-150. https://doi.org/10.3390/quantum1020013

Superposition Principle and Born’s Rule in the Probability Representation of Quantum States

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