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.

On the tomographic picture of quantum mechanics

MARMO, GIUSEPPE;SIMONI, ALBERTO;VENTRIGLIA, FRANCO
2010

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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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11588/367170
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