Some necessary conditions for quantum-state tomograms

Ya. A. Korennoy, Vladimir I. Man’ko

Shi-Min Xu, Xing-Lei Xu, Hongqi Li +1 more

M. R. Bazrafkan, E. Nahvifard

Sergio M. De Nicola, Renato Fedele, Margarita A. Man’ko +1 more

Ya. A. Korennoy, Vladimir I. Man’ko

It is shown that dynamical equations for quantum tomograms retain the normalization conditions of their solutions during evolution only if the solutions satisfy a set of special conditions. These conditions are found explicitly. On the contrary, it is also shown that the classical Liouville equation, Moyal equation for Wigner function, and evolution equation for Husimi function retain normalization of any initially normalized and quickly decaying at infinity functions on the phase space. Other necessary and sufficient conditions for optical and symplectic tomogram-like functions to be tomograms of physical states are discussed.

Grigori Gennadievich Amosov, Stefano Mancini, Vladimir I. Man’ko