Abstract
A review of new results in the quantumlike theory of an analytic signal (used in information processing) on the basis of the recently developed approach of the tomographic description of quantum states in quantum mechanics is presented. The procedure of noncommutative tomography of the analytic signal is used to study the analytic signal depending both on the spatial variable and the time. The entanglement theory of the analytic signal in the noncommutative‐tomography scheme is discussed in connection with information processing, and the possibility to use optical fibers for the simulation of quantum entanglement relevant to quantum computing is suggested.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
S. Mancini, V. I. Man'ko, and P. Tombesi, Phys. Lett. A, 213, 1 (1996).
S. Mancini, V.I. Man'ko, and P. Tombesi, Found. Phys., 27, 801 (1997).
Olga Man'ko and V.I. Man'ko, J. Russ. Laser Res., 18, 407 (1997).
Olga Man'ko and V.I. Man'ko, J. Russ. Laser Res., 20, 67 (1999).
M. A. Leontovich, Izv. Akad. Nauk SSSR, Ser. Fiz., 8, 16 (1944).
V. A. Fock and M. A. Leontovich, Zh. ´Eksp. Teor. Fiz., 16, 557 (1946).
J. A. Arnaud, Beam and Fiber Optics, Academic Press, New York (1976).
J. Sanchez Mondragon and K.-B. Wolf (eds.), Lie Methods in Optics, Lecture Notes in Physics, Springer, Berlin (1986), Vol. 250.
K.-B. Wolf (ed.), Lie Methods in Optics II, Lecture Notes in Physics, Springer, Berlin (1989), Vol. 352.
M. A. Man'ko and G. T. Mikaelyan, Sov. J. Quantum Electron., 16, 895 (1986).
M. A. Man'ko and G. T. Mikaelyan, “Modes and mode conversions in active semiconductor waveguides,” in: Nonlinear Optics of Semiconductor Lasers, Proceedings of the P.N. Lebedev Physical Institute, Nauka (Moscow), Vol. 166, p. 126 [Nova Science, Commack, New York (1987), Vol. 166, p. 170].
M. A. Man'ko, “Some aspects of nonlinear optics of semiconductor lasers,” in: M. Bertolotti (ed.), ECOOSA-90 Quantum Optics, IOP Publishing House, Bristol (1991), p. 247.
L. M. Brekhovskikh, Waves in Slab Media [in Russian], Nauka, Moscow (1973).
R. Fedele, M. A. Man'ko, and V. I. Man'ko, J. Russ. Laser Res., 21, 1 (2000).
R. Fedele, M. A. Man'ko, and V. I. Man'ko, J. Opt. Soc. Am. A, 17, 2506 (2000).
R. Fedele and P. K. Shukla (eds.), Quantumlike Models and Coherent Effects, World Scientific, Singapore (1995).
S. De Martino, S. De Nicola, S. De Siena, R. Fedele, and G. Miele (eds.), New Perspectives in the Physics of Mesoscopic Systems. Quantumlike Descriptions and Macroscopic Coherent Phenomena, World Scientific, Singapore (1997).
M. A. Man'ko, “Quantum-tomography method in information processing,” Contribution to the Fifth International Conference on Quantum Communication, Measurement, and Computing (Capri, Italy, 3-8 July 2000), in: O. Hirota and P. Tombesi (eds.), The QCM&C Proceedings, Kluwer Academic/Plenum Publishers, New York (2001, in press).
M. A. Man'ko, “Noncommutative tomography of analytic signal and entanglement in the probability representation of quantum mechanics,” Talk at the Second Bielefeld Workshop on Quantum Information and Complexity (Bielefeld, Germany, 12-14 October 2000); Eprint No. 2000/006 of the Workshop “The Sciences of Complexity: From Mathematics to Technology to a Sustainable World” (Center for Interdisciplinary Research, Bielefeld, Germany, 1 October 2000 - 31 August 2001) [http: //www.uni-bielefeld.de/ZIF/complexity/publications.html].
M. A. Man'ko, “Quantumlike models in beam physics and signal analysis,” Talk at the 18th Advanced ICFA Beam Dynamics Workshop om Quantum Aspects of Beam Physics (Capri, Italy, 15-20 October 2000), in: P. Chen (ed.), The QABP2k Proceedings, World Scientific, Singapore (2001, in press); Eprint No. 2000/007 of the Workshop “The Sciences of Complexity: From Mathematics to Technology to a Sustainable World” (Center for Interdisciplinary Research, Bielefeld, Germany, 1 October 2000 - 31 August 2001) [http: //www.uni-bielefeld.de/ZIF/complexity/publications.html].
M. A. Man'ko, J. Russ. Laser Res., 22, 48 (2001).
L. Cohen, J. Math. Phys., 7, 781 (1966).
L. Cohen, Proc. IEEE, 77, 941 (1989).
L. Cohen, IEEE Trans. Signal Process., 41, 3275 (1993).
K.-B. Wolf, Integral Transforms in Science and Engineering, Plenum Press, New York (1979).
M. A. Man'ko, V. I. Man'ko, and R. Vilela Mendes, “Tomograms and other transforms: A unified view,” Eprint math-ph/0101025 (2001); J. Phys. A (2001, in press).
M. A. Man'ko, J. Russ. Laser Res., 20, 225 (1999).
M. A. Man'ko, J. Russ. Laser Res., 21, 411 (2000).
V.I. Man'ko and R.V. Mendes, “Noncommutative time-frequency tomography of analytic signal,” SISSA-LANL Eprint Physics/9712022 Data Analysis, Statistics, and Probability.
V. I. Man'ko and R. V. Mendes, Phys. Lett. A, 263, 53 (1999).
E. Wigner, Phys. Rev., 40, 749 (1932).
J. Ville, Cables et Transmission, 2, 61 (1948).
A. Einstein, B. Podolsky, and N. Rosen, Phys. Rev., 47, 777 (1935).
M. A. Man'ko, V. I. Man'ko, and R. Vilela Mendes, “Quantum computation by quantumlike systems,” Eprint quant-ph/0104023 (2001).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Man'ko, M.A. Noncommutative Tomography of an Analytic Signal and Entanglement in the Probability Representation of Quantum Mechanics. J Russ Laser Res 22, 168–174 (2001). https://doi.org/10.1023/A:1011312122911
Issue Date:
DOI: https://doi.org/10.1023/A:1011312122911