On the Tomographic Picture of Quantum Mechanics
arXiv:1004.0102 · doi:10.1016/j.physleta.2010.04.056
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.
10 pages,latex,submitted to Physics Letters A
References in corpus (6)
- Symplectic tomography as classical approach to quantum systems
- An introduction to the tomographic picture of quantum mechanics
- Classical-Like Description of Quantum Dynamics by Means of Symplectic Tomography
- Reconstructing the density operator by using generalized field quadratures
- On the meaning and interpretation of Tomography in abstract Hilbert spaces
- A tomographic setting for quasi-distribution functions
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- On the tomographic description of classical fields
- Quantum Mechanics as Asymptotics of Solutions of Generalized Kramers Equation
- The Landau Problem and non-Classicality
- Quantum Tomography and the Quantum Radon Transform
- Entropic and information inequality for nonlinearly transformed two-qubit X-states