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

Voir la notice de l'article provenant de la source Math-Net.Ru

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/}
}
TY  - JOUR
AU  - G. G. Amosov
AU  - A. I. Dnestryan
TI  - Reconstruction of a~pure state from incomplete information on its optical tomogram
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2013
SP  - 62
EP  - 67
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2013_3_a6/
LA  - ru
ID  - IVM_2013_3_a6
ER  - 
%0 Journal Article
%A G. G. Amosov
%A A. I. Dnestryan
%T Reconstruction of a~pure state from incomplete information on its optical tomogram
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2013
%P 62-67
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2013_3_a6/
%G ru
%F IVM_2013_3_a6
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/

[1] Mancini S., Man'ko V. I., Tombesi P., “Wigner function and probability distribution for shifted and squeezed quadratures”, Quantum Semiclass. Opt., 7:4 (1995), 615–624 | DOI | MR

[2] Pauli W., “Die allgemeinen Prinzipien der Wellenmechanik”, Handbuch der Physik, 24 (1933), 83–272 | Zbl

[3] Orlowski A., Paul H., “Phase retrieval in quantum mechanics”, Physical Review A, 50:2 (1994), 921–924 | MR

[4] Leonhardt U., Munroe M., “Number of phases required to determine a quantum state in optical homodyne tomography”, Physical Review A, 54:4 (1996), 3682–3684 | DOI | MR

[5] Amosov G. G., Mancini S., Man'ko V. I., “On the information completeness of quantum tomograms”, Phys. Lett. A, 372:16 (2008), 2820–2824 | DOI | MR | Zbl

[6] Namias V., “The fractional order Fourier transform and its application to quantum mechanics”, J. Inst. Math. Appl., 25:3 (1980), 241–265 | DOI | MR | Zbl

[7] Amosov G. G., Dnestryan A. I., “O spektre semeistva integralnykh operatorov, opredelyayuschikh simplekticheskuyu kvantovuyu tomogrammu”, Tr. MFTI, 3:1 (2011), 5–9