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Tomography in abstract Hilbert spaces

V. I. Man'ko·G. Marmo·A. Simoni·F. Ventriglia
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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.

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BibTeXRIS

V. I. Man'ko, G. Marmo, A. Simoni, F. Ventriglia. 2006-04-06. Tomography in abstract Hilbert spaces. https://arxiv.org/abs/quant-ph/0604039

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