Quantum multiresolution analysis via fast Fourier transform on Heisenberg group

Ekaterina Rundblad; Valeriy G. Labunets; Peter Novak

doi:10.1117/12.603731

28 March 2005 Quantum multiresolution analysis via fast Fourier transform on Heisenberg group

Ekaterina Rundblad; Valeriy G. Labunets; Peter Novak

Author Affiliations +

Proceedings Volume 5813, Multisensor, Multisource Information Fusion: Architectures, Algorithms, and Applications 2005; (2005) https://doi.org/10.1117/12.603731
Event: Defense and Security, 2005, Orlando, Florida, United States

Abstract

We study classical and quantum harmonic analysis of phase space functions (classical observes) on finite Heisenberg group HW_2N+1(Z^N_mn, Z^N_mn, Z_mn) over the ring Z_mn. This group is the discrete version of the real Heisenberg group HW_2N+1(R^N, R^N, R), 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 1D 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.

Citation Download Citation

Ekaterina Rundblad, Ekaterina Rundblad, Valeriy G. Labunets, Valeriy G. Labunets, Peter Novak, Peter Novak, } "Quantum multiresolution analysis via fast Fourier transform on Heisenberg group", Proc. SPIE 5813, Multisensor, Multisource Information Fusion: Architectures, Algorithms, and Applications 2005, (28 March 2005); doi: 10.1117/12.603731; https://doi.org/10.1117/12.603731

ACCESS THE FULL ARTICLE

PERSONAL SIGN IN
Full access may be available with your subscription

Email or Username Forgot your username?

Password Forgot your password?

Show

Remember Email/Username on this computer

Remember Password

No SPIE account? Create an account
or Institutional Sign In via Shibboleth

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available

Members: $14.40

Non-members: $18.00 ADD TO CART

Show All Keywords

Keywords/Phrases

Search In:

Publication Years