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arXiv · 2508.08456

From free-evolution to tomographic representation

Sergio Cordero·Ramón López-Peña·Eduardo Nahmad-Achar·Octavio Castaños·Julio Aberto López-Saldívar·Vladimir I. Man'ko
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Abstract

We use the free evolution propagator to determine the quantum probability representation (i.e., the general expression of the tomogram) of any one-dimensional system described by a density state. The evolution operator for the considered quantum system is additionally used to establish the corresponding time dependent tomogram. Applications are given for a Gaussian wave packet, the quantum shutter related with the phenomenon of diffraction in time, the double quantum shutter, and a finite potential. A generalisation to describe $N$ particle systems is also presented and, in particular, we find the tomogram associated to the 2 particle case occupying in general non-orthogonal states. In the latter case, for a bipartite quantum system, the entanglement properties are established by considering quantum information concepts such as the linear entropy.

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Sergio Cordero, Ramón López-Peña, Eduardo Nahmad-Achar, Octavio Castaños, Julio Aberto López-Saldívar, Vladimir I. Man'ko. 2025-08-11. From free-evolution to tomographic representation. https://arxiv.org/abs/2508.08456

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