Tomography of Spin States and Classical Formulation of Quantum Mechanics

Alberto Ibort, Vladimir I. Man’ko, Giuseppe Marmo +2 more

V. A. Andreev, Vladimir I. Man’ko

A new “classical” formulation of conventional quantum mechanics is used to construct a description of quantum states with spin j =1/2 which uses only positive classical probabilities of observables instead of a complex density matrix. These probabilities are functions of points on a unit sphere which determine the directions relative to which the spin projections are measured. The proposed construction is a generalization of a system for tomography of the spin states of a single particle and may be used as a new method of measuring two-particle spin states. For pure spin states this method is exactly the same as the case of a single particle. Additional probabilities must be defined to describe mixed states.

A. V. Kusev, Olga V. Man’ko, Nicolaii V. Tcherniega

Notion of distance between quantum states is reviewed using Hellinger distance between probability distributions and classical formulations of quantum mechanics based on tomography scheme. The Hellinger distances between the states of damped oscillator (considered in the frame of Caldirola-Kanai model) with delta-kicked frequencies in the regime of weak and strong damping, between the photon number distribution functions in SRS process, and between spin tomograms are considered.

Oliver Dial

Vladimir I. Man’ko

Vladimir I. Man’ko

A review of the new formulation of quantum mechanics in which the tomographic probability describes the quantum state instead of the wave function is presented. The tomographic probability in classical statistical mechanics is considered. The superposition principle is discussed.