On the Tomographic Picture of Quantum Mechanics
A. Ibort, V.I. Man'ko, G. Marmo, A. Simoni, F. Ventriglia
TL;DR
This paper establishes criteria for symplectic tomograms to uniquely determine quantum states and links them to Naimark positive-definite functions, enhancing the understanding of quantum state reconstruction in the probability representation.
Contribution
It introduces necessary and sufficient conditions for symplectic tomograms to represent quantum states and connects tomographic reconstruction with Naimark positive-definite functions.
Findings
Criteria for symplectic tomograms to determine quantum states
Connection between tomographic reconstruction and Naimark functions
Properties ensuring tomograms describe quantum states
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.
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