Next Article in Journal / Special Issue
Resource Theories of Nonclassical Light
Previous Article in Journal
Everett’s Multiverse and the World as Wavefunction
Previous Article in Special Issue
Selective Engineering for Preparing Entangled Steady States in Cavity QED Setup
Open AccessArticle

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

Lebedev Physical Institute, Leninskii Prospect 53, Moscow 119991, Russia
*
Author to whom correspondence should be addressed.
Based on the talk presented by Margarita A. Man’ko at the 16th International Conference on Squeezed States and Uncertainty Relations {ICSSUR} (Universidad Complutense de Madrid, Spain, 17–21 June 2019).
Quantum Reports 2019, 1(2), 130-150; https://doi.org/10.3390/quantum1020013
Received: 5 September 2019 / Revised: 18 September 2019 / Accepted: 20 September 2019 / Published: 26 September 2019
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. View Full-Text
Keywords: entanglement; interference phenomenon; superposition of quantum states; quantum tomograms entanglement; interference phenomenon; superposition of quantum states; quantum tomograms
Show Figures

Graphical abstract

MDPI and ACS Style

Doskoch, I.Y.; Man’ko, M.A. Superposition Principle and Born’s Rule in the Probability Representation of Quantum States. Quantum Reports 2019, 1, 130-150.

Show more citation formats Show less citations formats

Article Access Map by Country/Region

1
Back to TopTop