The Discrete Center-of-Mass Tomogram

Olga V. Man’ko, Vladimir I. Man’ko

Ashot S. Avanesov, Vladimir I. Man’ko

We adopt methods of symplectic tomography and discrete phase space for the description of states of discrete variable quantum systems (qudits). The proposed tomographic functions are constructed as generalized analogs of the center-of-mass and the cluster tomograms and associated with finite linear manifolds in the discrete phase space. Hilbert spaces of considered qudits must have the power of a prime dimension, so the corresponding phase spaces are the vector spaces over finite fields. We find conditions for the nonnegativity of the constructed functions and obtain formulae for the density matrix restoration.

James M. McCracken

Ivan V. Dudinets, Margarita A. Man’ko, Vladimir I. Man’ko

We review the formalism of center-of-mass tomograms, which allows us to describe quantum states in terms of probability distribution functions. We introduce the concept of separable and entangled probability distributions for center-of-mass tomography. We obtain the time evolution of center-of-mass tomograms of entangled states of the inverted oscillator.

Margarita A. Man’ko

The tomographic entropy for center-of-mass tomograms is introduced for multimode electromagnetic-field states. The entropic uncertainty relations are obtained for the quantum tomograms. A comparison of quantum states with the classical electromagnetic-field states in the context of the entropic uncertainty relations is presented.

Federica Agostini