Quantum-state tomogram from s-parameterized quasidistributions

E. Nahvifard, M. R. Bazrafkan

Margarita A. Man’ko

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

Vladimir I. Man’ko, Liubov A. Markovich

We consider tomograms and quasidistributions, such as the Wigner functions, the Glauber–Sudarshan P-functions, and the Husimi Q-functions, that violate the standard normalization condition for probability distribution functions. We introduce special conditions for theWigner function to determine the tomogram with the Radon transform and study three different examples of states like the de Broglie plane wave, the Moshinsky shutter problem, and the stationary state of a charged particle in a uniform constant electric field. We show that their tomograms and quasidistribution functions expressed in terms of the Dirac delta function, the Airy function, and Fresnel integrals violate the standard normalization condition and the density matrix of the state therefore cannot always be reconstructed. We propose a method that allows circumventing this problem using a special tomogram in the limit form.

Margarita A. Man’ko

Integral transforms of analytic signal and quantum-system states like wavelets, tomograms, Ville-Wigner and other quasidistributions are constructed for systems with several degrees of freedom. Mutual relations of the integral transforms are presented. Quantum propagator is interpreted as the kernel of the integral transform. An example of the integral transforms with generic Gaussian kernels is studied. The fractional Fourier transform is discussed.

Muhammad Hamza Waseem, Faizan-e-Ilahi, Muhammad Sabieh Anwar