The tomographic description of a quantum state is formulated in an abstract infinite-dimensional Hilbert space framework, the space of the Hilbert-Schmidt linear operators, with trace formula as scalar product. Resolutions of the unity, written in terms of over-complete sets of rank-one projectors and of associated Gram-Schmidt operators taking into account their non-orthogonality, are then used to reconstruct a quantum state from its tomograms. Examples of well known tomographic descriptions illustrate the exposed theory.

Tomography in abstract Hilbert spaces / V. I., Man'Ko; Marmo, Giuseppe; Simoni, Alberto; Ventriglia, Franco. - In: OPEN SYSTEMS & INFORMATION DYNAMICS. - ISSN 1230-1612. - STAMPA. - 13:3(2006), pp. 239-253. [10.1007/s11080-006-9004-4]

Tomography in abstract Hilbert spaces.

MARMO, GIUSEPPE;SIMONI, ALBERTO;VENTRIGLIA, FRANCO
2006

Abstract

The tomographic description of a quantum state is formulated in an abstract infinite-dimensional Hilbert space framework, the space of the Hilbert-Schmidt linear operators, with trace formula as scalar product. Resolutions of the unity, written in terms of over-complete sets of rank-one projectors and of associated Gram-Schmidt operators taking into account their non-orthogonality, are then used to reconstruct a quantum state from its tomograms. Examples of well known tomographic descriptions illustrate the exposed theory.
2006
Tomography in abstract Hilbert spaces / V. I., Man'Ko; Marmo, Giuseppe; Simoni, Alberto; Ventriglia, Franco. - In: OPEN SYSTEMS & INFORMATION DYNAMICS. - ISSN 1230-1612. - STAMPA. - 13:3(2006), pp. 239-253. [10.1007/s11080-006-9004-4]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11588/204238
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