Tomography in abstract Hilbert spaces
量子物理
2007-05-23 v1 高能物理 - 理论
数学物理
math.MP
摘要
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.
引用
@article{arxiv.quant-ph/0604039,
title = {Tomography in abstract Hilbert spaces},
author = {V. I. Man'ko and G. Marmo and A. Simoni and F. Ventriglia},
journal= {arXiv preprint arXiv:quant-ph/0604039},
year = {2007}
}
备注
16 pages, presented at Palermo "TQMFA2005" Conference. To appear on "Open Systems & Information Dynamics" (2006)