Quantum multiresolut ion analysis via fast Fourier transforms on Heisenbrg finite group / Rundblad E., Labunets V., Novak P. // Proceedings of SPIE - The International Society for Optical Engineering. - 2005. - V. 5813, l. . - P. 301-311.

ISSN:
0277786X
Type:
Conference Paper
Abstract:
We study classical and quantum harmonic analysis of phase space functions (classical observes) on finite Heisenberg group HW2N+1 (Z mn,N, Zmn) over the ring Zmn. This group is the discrete version of the real Heisenberg group HW2N+1 (RN, RNR), where R is the real field. These functions have one dimensional and m1, m2,..., mn-dimensions matrix valued spectral components (for irreducible representations of HW 2N+1. The family of all ID representations gives classical world world (CW). Various mi-dimension representations (i = 1, 2,..., n) map classical world (CW) into quantum worlds QW(mi) of ith resolution (i = 1, 2,..., n). Worlds QW(m1) and QW(mn) contain rough information and fine details about quantum word, respectively. In this case the Fourier transform on the Heisenberg group can be considered as Weyl quantization multiresolution procedure. We call this transform the natural quantum Fourier transform.
Author keywords:
Classical/quantum interface; Fast fourier transform; Heisenberg group; Multiresolution analysis; Quantum computing; Weyl quantization
Index keywords:
Computation theory; Fast Fourier transforms; Harmonic analysis; Optical resolving power; Classical/quantum interface; Heisenberg group; Multiresolution analysis; Quantum computing; Weyl quantization;
DOI:
10.1117/12.603731
Смотреть в Scopus:
https://www.scopus.com/inward/record.uri?eid=2-s2.0-27544508540&doi=10.1117%2f12.603731&partnerID=40&md5=e6275d11ffe69dbbef4aee54339bcdb5
Соавторы в МНС:
Другие поля
Поле Значение
Art. No. 32
Link https://www.scopus.com/inward/record.uri?eid=2-s2.0-27544508540&doi=10.1117%2f12.603731&partnerID=40&md5=e6275d11ffe69dbbef4aee54339bcdb5
Affiliations EnerSoft Inc., FL, United States
Author Keywords Classical/quantum interface; Fast fourier transform; Heisenberg group; Multiresolution analysis; Quantum computing; Weyl quantization
References Berezin, F.A., Quantization (1974) Math. USSR Izvestija, 8, pp. 1109-1165; Coburn, L.A., Berezin-Toeplitz quantization (1994) Algebraic Methods in Operator Theory, pp. 101-108. , Birhkhauser, New Yokr; Folland, G.B., (1989) Harmonic Analysis in Phase Space, , Princeton University Pres, Princeton, New Jersey; Kisil, V.V., Arellano, E.R., (1994) The Riesz-clifford Functional Calculus for Non-commuting Operators and Quantum Field Theory, 20p. , Reporte Interne # 166, Departamento de Mathematicas CINVESTAV del IPN, Mexico City; Kirilov, A.A., (1990) Geometric Quantization, pp. 137-172. , Vol. 4 of Encyclopedia of Mathematical Sciences, Springer-Verlag, Berlin; Doran, R., (1994) C* -Algebras: 1943-1993, , No. 167 in Contemporary Mathematics. AMS, Providence, Rhode Island; Scubin, M.A., (1987) Pseudodifferential Operators and Spectral Theory, , Springer-Verlag, Berlin; Coburn, L.A., Xia, J., Toeplitz algebras and Rieffel deformation (1994) Comm. Math. Phys.; Howe, R., On the role of the Heisenberg group in harmonic analysis (1980) Bull, of the AMS (New Series), 3 (2), pp. 821-843; Howe, R., Quantum mechanics and partial differential equations (1980) J. Func. Anal., 38, pp. 188-254; Weyl, H., (1931) The Theory of Groups and Quantum Mechanics, , Dover, New York; Serre, J.-P., (1977) Linear Representations of Finite Groups, , Springer-Verlag, New York; Terras, A., (1999) Fourier Analysis on Finite Groups and Applications, , Cambridge University Press, Cambridge; Labunets-Rundblad, E.V., Labunets, V.G., Fast fourier-weyl transform (2000) Signal Processing X, Theories and Applications, pp. 505-508. , Eusipcc-2000, Tampere, Finland, 4-8 September; Labunets-Rundblad, E.V., Labunets, V.G., Fast Fourier-Weyl-Heisenberg transforms (2000) Signal Processing X, Theories and Applications, pp. 2353-2356. , Eusipco-2000, Tampere, Finland, 4-8 September; Labunets, V.G., Rundblad-Labunets, E.V., Astola, J., Fast quantum Fourier-Weyl-Heisenberg transforms (2001) SPIE Aerospace/Defense Sensing, Simulation, and Controls. Conf. "Quantum Computing II", , 16-20 April 2001, Orlando, Florida, USA; Labunets-Rundblad, E.V., Labunets, V.G., Astola, J., Egiazarian, K., Fast Fourier-Heisenberg transforms (2000) IEEE Inter. Conf. on ASSP, pp. 540-543. , June 5-9, Istanbul, Turkey; Labunets, V.G., Labunets-Rundblad, E.V., Astola, J., Introduction to quantum and hyperquantum information tecnologies. P.1: Real probability and unreal probabilities (2000) Proc. of First International Workshop on Spectral Tecniques and Logic Design for Future Digital Systems, pp. 283-321. , Tampere, Finland, June 2-3; Labunets, V.G., Rundblad-Labunets, E.V., Astola, J., Fast quantum nD Fourier and Radon transforms Applied Geometrical Algebras in Computer Science and Engineering. AGACSE 2001, Cambridge, UK; Labunets, V.G., Rundblad-Labunets, E.V., Astola, J., Fast classical and quantum fractional Haar wavelet transforms (2001) Image and Signal Processing Ana Analysis ISPA'Ol, June 19-21, Pula, Croatia; Labunets, V.G., Rundblad-Labunets, E.V., Astola, J., Fast classical and quantum fractional Walsh transforms (2001) Image and Signal Processing Ana Analysis ISPA '01, June 19-21, Pula, Croatia; Labunets, V.G., Rundblad-Labunets, E.V., Astola, J., Superfast quantum nD Fourier and Radon transforms (2001) SPIE Aerospace/Defense Sensing, Simulation, and Controls. Conf. "Quantum Computing II", , 16-20 April 2001, Orlando, Florida, USA; Labunets, V.G., Rundblad-Labunets, E.V., Astola, J., Fast quantum Fourier-Weyl-Heisenberg transforms Applied Geometrical Algebras in Computer Science and Engineering. AGACSE 2001, Cambridge, UK; Labunets, V.G., Rundblad, E.V., Astola, J., Is the brain a "Clifford algebra quantum computer"? Applied Geometrical Algebras in Computer Science and Engineering. AGACSE 2001, Cambridge, UK
Correspondence Address EnerSoft Inc., FL, United States; email: krundblad@enersoft.com
Editors Dasarathy B.V.
Sponsors SPIE - The International Society for Optical Engineering
Conference name Multisensor, Multisource Information Fusion: Architecture, Algorithms, and Applications 2005
Conference date 30 March 2005 through 31 March 2005
Conference location Orlando, FL
Conference code 65928
CODEN PSISD
Language of Original Document English
Abbreviated Source Title Proc SPIE Int Soc Opt Eng
Source Scopus