On the tomographic picture of quantum mechanics

2010/04/01 by A. Ibort, Alberto Ibort, V. I. Man'ko +4
Mathematics · Physics and Astronomy · #Mathematical Analysis and Transform Methods #Quantum Mechanics and Applications #advanced mathematical theories #quant-ph

paper · pdf · doi:10.1016/j.physleta.2010.04.056

published as Phys.Lett.A374:2614-2617,2010 · 10 pages,latex,submitted to Physics Letters A

arxiv created 2010/04/01 · openalex publication_date 2010/04/23 · arxiv updated 2010/05/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We formulate necessary and sufficient conditions for a symplectic tomogram of a quantum state to determine the density state. We establish a connection between the (re)construction by means of symplectic tomograms with the construction by means of Naimark positive-definite functions on the Weyl-Heisenberg group. This connection is used to formulate properties which guarantee that tomographic probabilities describe quantum states in the probability representation of quantum mechanics.

Citations

• Reconstructing the density operator by using generalized field quadratures
• On the meaning and interpretation of tomography in abstract Hilbert spaces
• On the Quantum Correction For Thermodynamic Equilibrium