Dynamics of System States in the Probability Representation of Quantum Mechanics

Abstract

A short description of the notion of states of quantum systems in terms of conventional probability distribution function is presented. The notion and the structure of entangled probability distributions are clarified. The evolution of even and odd Schrödinger cat states of the inverted oscillator is obtained in the center-of-mass tomographic probability description of the two-mode oscillator. Evolution equations describing the time dependence of probability distributions identified with quantum system states are discussed. The connection with the Schrödinger equation and the von Neumann equation is clarified.

Probability Distributions Describing Qubit-State Superpositions

“…In this paper, we consider the two-dimensional Hilbert spaces (examples of qubits) and four-dimensional Hilbert spaces (examples of ququarts); for infinite-dimensional probability representations (tomograms), see [32].…”

Even and Odd Cat States of Two and Three Qubits in the Probability Representation of Quantum Mechanics

“…Recently, probability representations called symplectic tomograms have been determined for several important states of the harmonic oscillator, including thermal states [ 22 ], coherent states, Fock states [ 8 ], and Schrödinger cat states [ 23 ], which were originally introduced under the name even and odd coherent states. The time evolution of these tomograms, initially prepared in the potential of the usual harmonic oscillator, has also been derived for free particle motion [ 6 , 8 , 22 , 23 ] or for inverted oscillators [ 24 , 25 , 26 ].…”