Tomography in abstract Hilbert spaces

Details Tomography in abstract Hilbert spaces Tomography in abstract Hilbert spaces

2006-04-06

arxiv.org/abs/quant-ph/0604039v1

Physics

Quantum Physics

16 pages, presented at Palermo "TQMFA2005" Conference. To appear on "Open Systems & Information Dynamics" (2006)

Scientific paper

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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