Geodesic
Reconstruction of a~pure state from incomplete information on its optical tomogram
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2013), pp. 62-67

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We consider the problem of reconstructing a state (i.e., a positive unit-trace operator) from incomplete information on its optical tomogram. In the case, when a (pure) state is determined by a function representing a linear combination of $N$ ground and excited states of a quantum oscillator, we propose a technique for reconstructing this state from $N$ values of its tomogram. For $N=3$ we find an exact solution to the problem under consideration.
Keywords: state, optical tomogram, eigenfunctions of integral operator. 
@article{IVM_2013_3_a6,
     author = {G. G. Amosov and A. I. Dnestryan},
     title = {Reconstruction of a~pure state from incomplete information on its optical tomogram},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {62--67},
     publisher = {mathdoc},
     number = {3},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2013_3_a6/}
}
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G. G. Amosov; A. I. Dnestryan. Reconstruction of a~pure state from incomplete information on its optical tomogram. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2013), pp. 62-67. http://geodesic.mathdoc.fr/item/IVM_2013_3_a6/